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UNITED STATES OF AMERICA. 



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THE CREDENTIALS OF SCIENCE 
THE WARRANT OF FAITH. 



THE 



Credentials of Science 



THE WARRANT OF FAITH. 



BY 



JOSIAH PARSONS COOKE, LL.D., 

ERVING PROFESSOR OF CHEMISTRY AND MINERALOGY IN 
HARVARD UNIVERSITY. 



SECOND EDITION. 




NEW YORK: 
APPLETON AND COMPANY. 

1893- 



^^7?i^y' 



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Copyright, 1888, 
By ROBERT CARTER AND BROTHERS. 

Copyright, 1893, 
By JOSIAH p. COOKE. 



IN MEMORIAM 

Eostoell Btoigf)t l^ttcJjcocft. 

"qui docti fuerint fulgebunt quasi splendor firmamenti; 

et qui ad justitiam erudiunt multos, quasi 

stella in perpetuas ^ternitates." 



PREFACE TO SECOND EDITION. 



THE subject of this volume was first developed 
by the author as a course of lectures at the 
invitation of the Union Theological Seminary of 
New York City, and the lectures were delivered in 
the Adams Chapel of the Seminary during the early 
spring of 1887, the course oif eight lectures closing 
on Easter Eve. The course was given on a founda- 
tion established by Mr. Zebulon Stiles Ely to sup- 
port a lectureship on the Evidences of Christianity. 
The material was subsequently considerably ampli- 
fied, and delivered as a course of twelve lectures 
before the Lowell Institute of Boston, closing on 
Christmas Eve of the same year. The lectures have 
been printed as thus extended, although in some 
cases the limitations of a lecture hour compelled 
a division of subjects, which are here united under 
the same heading, thus reducing the number of 
chapters in the book to ten. 

The motive of the work is indicated by the title, 
the chief argument being that the popular objec- 
tions to Christian beliefs might be urged with equal 
force against each of the predominant systems of 



Vlll PREFACE TO SECOND EDITION. 

science of the present day, and are the necessary 
result of the limitations of our human knowledge ; 
that so far from proving the inconsequence of our 
religious beliefs, the oppositions so greatly magnified 
plainly point to a condition in which the limitations 
that now narrow our vision will be removed. In 
following out this argument the author has discussed 
the basis of scientific systems ; the modes of thought 
distinguished as induction and deduction, by which 
general principles have been apprehended and their 
scope constantly widened ; the significance of the so- 
called laws of Nature ; the validity of the prevailing 
theories or systems of science ; and the predominant 
principles of scientific thought. 

By the terms of the appointment to the Ely Lec- 
tureship the copyright of this book was vested in 
the Union Theological Seminary, and the first edition 
was published by Robert Carter and Brothers, under 
the auspices of the Seminary; but after that firm 
retired from business, the directors of the Seminary, 
by vote at a meeting held on November lo, 1891, 
transferred the copyright to the author, who has 
carefully revised the work for a new edition. No 
important changes have been made in the form of 
the argument or in the mode of presentation, but 
the text has been revised, and misprints, as far as 
discovered, corrected. 

Cambridge, April 22, i8gj. 



CONTENTS. 



Lecture Page 

I. The Argument of Natural Theology . . i 

II. Preparing the Way 29 

III. The Induction of Newton 59 

IV. Deduction 93 

V. Examples of Scientific Investigation . . 127 

VL Laws of Nature 158 

VII. Determinate and Indeterminate Laws . , 184 

VIII. Theories or Systems of Science .... 209 

IX. Predominant Principles of Scientific 

Thought 260 

X. The Systems Compared. — Religion and 

Science , . , 289 



THE CREDENTIALS OF SCIENCE 
THE WARRANT OF FAITH. 



LECTURE I. 

THE ARGUMENT OF NATURAL THEOLOGY. 

NATURAL Religion is as old as man's conscious- 
ness of dependence, and Natural Theology is 
coeval with literature. Its fundamental arguments 
were urged by the Greek and Roman philosophers, 
and the illustrations of the subject by Galen have 
scarcely been equalled in modern times. During 
the last two centuries works on natural theology 
have formed a conspicuous feature in English litera- 
ture, — in consequence chiefly of several pious foun- 
dations which have provided for the discussion of the 
subject at stated intervals. These works have as a 
rule been written in a popular style, and have dealt 
with illustrations of old arguments rather than with 
the arguments themselves. They have served an ex- 
cellent purpose by keeping before the popular mind 
the ever accumulating mass of evidence of skill and of 
plan which nature offers, and by exhibiting the reli- 
gious aspects of scientific facts and theories. Unfor- 



2 THE ARGUMENT OF NATURAL THEOLOGY. 

tunately they have often been open to criticism, and 
too frequently have justified the contempt into which 
teleology has so generally fallen. 

A recent writer, in his " Critique of Design Argu- 
ments," ^ has done an excellent work, not only by fix- 
ing attention on the arguments, but also by furnishing 
a carefully prepared synopsis of all the important 
writings bearing on natural theology from the earliest 
times. But while freely admitting the justice of this 
writer's criticism in many respects, even when we our- 
selves have fallen under the ban, we cannot concur 
with him either in his general estimate of design argu- 
ments, or in the essential character of the distinction 
which he seeks to draw between the argument from 
general plan and the so-called argument from design. 
This last phrase has become one of the universal 
terms of our language, and it is not to be supposed 
that acute Scotch logicians like Dugald Stewart and 
Reid overlooked the obvious begging of the question 
which a precise definition of the words would involve. 
There has been undoubtedly as frequent misuse of 
language in essays on natural theology as in similar 
popular expositions ; but much of this has resulted 
from the necessities of the case. 

In popular discourse language cannot be used with 
the precision of mathematical term.s, and often a 
hypercritical spirit defeats the main object of the 
teacher. Singular as it is, the more a man knows, the 
more difificult it becomes to present a subject in lan- 
guage that can be easily comprehended. The teacher 

1 Critique of Design Arguments, by L. E. Hicks. New York. 
Charles Scribner's Sons, 1883. 



DESIGN SUPPOSES A DESIGNER. 



is hampered by his knowledge of the limitations to 
the general propositions he enunciates, and he is 
forced to avail himself of all the latitude which the 
most liberal interpretation of language will allow. 
No one who has not had the experience knows how 
difficult it often is to reconcile exact accuracy with 
that concise statement which is one of the essential 
conditions of effective teaching; and the intended pur- 
port of rhetorical writing can always be misrepre- 
sented by the quotation of isolated passages. 

When an able theologian writes, " Design supposes 
a designer," it is reasonable to infer that he does not 
intend to involve his readers in the logical absurdity 
of an identical proposition, but simply intends to de- 
clare the undoubted fact, that a multitude of relations 
in nature suggest to the mind of man an intelligent 
author. 

The confusion implied in this and in similar phrase- 
ology arises from an attempt to gauge such reason- 
ing by the rules of deductive logic. Man has not 
risen to knowledge of Divine things by deduction but 
by induction. These things always have been, and 
always will continue to be to the logical Greeks of 
every age foolishness, and so long as the theologian 
cherishes the conceit that the Godhead can be dem- 
onstrated, he cannot hope to escape from the web of 
logical fallacies which his argument must involve. 

The knowledge of God has come to man through 
nature precisely in the same way as the generaliza- 
tions of science, and is subject to the same limitations 
and carries the same conviction as all general truths. 
Man knows God by the same means and through the 



4 THE ARGUMENT OF NATURAL THEOLOGY. 

same sources that he knows the principles of gravita- 
tion, heat, and electricity. In each case an assumed 
energy acting through special channels under definite 
laws is the best explanation he can form of a certain 
class of phenomena. So also the assumption of an 
Intelligent Will, with power to create and power to 
sustain, is the commonly received explanation which 
man has formed of the origin and continuance of this 
universe in which he dwells. 

The fundamental principles of science may be said 
to be suggestions of nature confirmed by experience. 
When once conceived, we can often deduce from a 
general principle, mathematically or otherwise, a host 
of inferences which observation substantiates. This 
indeed is the normal way by which our knowledge of 
nature is enlarged ; and such deductions, verified by 
experience, furnish the strongest confirmation of the 
truth of the principle with which we started. But the 
principle itself was no deduction, it was a suggestion 
of nature ; and this is all we know of its origin. We 
may seek to study the conditions and circumstances 
under which such suggestions have come into the 
minds of the favored men of the race, but we get no 
nearer to the source. 

Among essential conditions we at once recognize 
a familiar acquaintance with nature, and a powerful 
but well regulated imagination. We also readily trace 
the influence of analogies, and even of accidental asso- 
ciations. We easily see anthropomorphic elements 
in such conceptions ; but all these things are merely 
accessories to a mental process of which the discoverer 
himself can give no clear account, as the trivial stories 



THE CONCEPTION OF GOD AN INDUCTION. 5 

of swinging lamps and falling apples so plainly show. 
It is a mental faculty which, though in its highest 
manifestation only known to a few highly gifted men, 
is in some small measure within the experience of 
every student of nature. To such students the 
method seems perfectly natural, even when they may 
not be able to discover its elements. Many philoso- 
phers, like Bacon, have attempted to analyze the 
method, and have named it " induction ; " but few of 
those who are in the habit of using the method would 
recognize the mechanism that has been described. 
The so-called induction resembles inspiration, and 
the loftiest inspiration seems to be only the same fac- 
ulty of mind more highly developed. 

As are the fundamental principles of science, so is 
the conception of God a suggestion of nature con- 
firmed by experience. It is an induction which com- 
mands belief, not a deduction which compels consent. 
This difference between inductive and deductive truth 
does not depend upon the degree of certitude, but on 
the completeness of knowledge. The highest truths 
can be known only in part, and it is such truths that 
are reached by induction. Thus alone can men " rise 
on stepping-stones of their dead selves to higher 
things." Moreover, of such truths certitude of con- 
viction comes only with experience. Christ said " If 
ye do my will ye shall know of the doctrine " and the 
principle thus announced applies to all inductive 
truths. 

It is only beliefs thus attested which command the 
enthusiasm of men. For such beliefs alone will men 
sacrifice their lives. The deductions of Geometry are 



RELIGION AND CHEMISTRY. 



great truths fully comprehended ; but how inconceiv- 
able, a martyr to the theorem of Pythagoras ! And 
there never would have been a martyr to religious be- 
liefs, if these verities could have been reached by de- 
duction, — in a word, could have been demonstrated. 

Regard now the fundamental truth of natural re- 
ligion as an induction, comprehended only in part, 
but having all the certitude which the experience of 
the ages has given, and your natural theology becomes 
a system which is not only consistent throughout, but 
which harmonizes with all knowledge. Attempt, how- 
ever, to claim for this truth deductive demonstration, 
and you at once involve your system in contradictions, 
and miss the very certitude you are seeking to secure. 

More than twenty-five years ago the writer de- 
livered a course of lectures at Brooklyn, on the Gra- 
ham Foundation, in which the position just defined 
was distinctly taken. These lectures were subse- 
quently published, and the book is well known under 
the title of'* Religion and Chemistry, or Proofs of God's 
Plan in the Constitution of the Atmosphere." The 
lectures were written for a popular audience, and there- 
fore in a rhetorical form, and it would be easy to mis- 
represent the argument by a quotation of isolated 
passages ; but no one who actually reads the book 
can mistake either the intentions of the writer or the 
spirit of his work. No one could have been more 
dissatisfied with the work than the author himself, 
and for this reason he suffered the book to remain 
out of print for many years ; and when after repeated 
requests from clerical friends the work was revised for 
the recent edition, the expository and rhetorical form 



CONFLICT BETWEEN SCIENCE AND THEOLOGY. 7 

was retained simply because in the judgment of these 
friends the usefulness of the book depended in no 
small measure on its popular style. Thus called upon 
to review what was written at a time when it might be 
expected that logic should be somewhat blinded by en- 
thusiasm, the writer could find nothing in the tenor or 
spirit of the work that he desired to change; and the 
general argument appears to him still, as it did at first, 
unanswerable. 

Now, however, that I am invited to address the 
members of this influential theological seminary on 
the same general subject, I feel that the best service 
I can render is to present the same argument in a 
more methodical and compact form, — a form in 
which its strength will better appear, and its weak- 
ness, if any, will be more conspicuously exposed. 
With no desire to magnify my office, I cannot but 
feel that the subject under discussion is one of great 
importance to theological students. It is the ground 
on which the conflict between science and theology 
has always been fought. Whatever may have been 
the incidental advantages, no one can question that the 
conflict itself is a great evil. Is it, indeed, necessary 
that the promulgation of every important doctrine of 
science should be followed by a partial eclipse of 
faith, like that through which so many minds have 
recently been passing? Brought as I have been into 
sympathy with the advocates on both sides, I believe 
I am in a position to form an impartial judgment; 
and while fully recognizing the narrowness and evil 
spirit which men even of large knowledge have often 
exhibited, I feel constrained to express the opinion that 
the clergy are largely responsible for the bad efl'ects 



8 THE ARGUMENT OF NATURAL THEOLOGY. 

of the controversy. Remember that science is para- 
mount in its own sphere, that its methods are legiti- 
mate, and its only object is truth ; and be assured 
that if any one of its devotees is irregular in his 
methods, or false to his profession, his own associates 
will be the first to criticise and condemn his errors. 
Moreover, the doctrines of science are held with 
great jealousy; and, although the evils of partisan- 
ship are as great in scientific controversies as else- 
where, the doctrines themselves will stand or fall 
solely on their own merit in the end. Once attested 
they cease to be safe subjects for the uninitiated to 
discuss, and much less, proper objects to anathema- 
tize. I can assure you that there have been times 
when the obligation which the church enjoins to hear 
sermons has been a painful duty to one who holds 
the truth in reverence, and desires also to reverence 
the defenders of the ** faith once delivered to the 
saints." I cannot but believe that if the clergy 
understood more fully the true relations of scientific 
doctrines, and saw clearly that the fundamental postu- 
late of theology rests on the same basis, they would 
be more patient with the inevitable friction which 
attends the progress of truth as well as the coming 
of the kingdom. 

In discussing the broad subject of natural theology ' 
the limitations of my own studies must necessarily 
constrain me to confine myself to those arguments 
which may be drawn from the facts of external na- 
ture ; and this I shall do without in the least under- 
valuing the purely ontological arguments based on 
the equally definite facts of consciousness. But let it 



DEVELOPMENT OF THE CONCEPTION OF GOD. 9 

also be clearly understood that I shall regard as a 
part of the phenomena of nature the undoubted his- 
torical facts of Christianity, as well as the clearly 
established facts connected with other rehgions; and 
in my opinion the evidences of natural theology are 
most incomplete when these all-important phenom- 
ena are left out of view. Of course such facts will 
be here studied in their objective, and not in their 
subjective aspect. 

By considering the development of the conception 
of God in the mind of man, I think we can gain some 
insight into the nature of the mental process by 
which the conception is reached, and in the same 
way that by the study of embryology we gain a 
better knowledge of animal structure. There can be 
no question that there are certain uniform stages in 
the order of this development, both in the history of 
the race and in the education of each individual 
man. This very uniformity under such diverse con- 
ditions plainly shows that the conception is not the 
accident of circumstances, but the normal product 
of the human mind under its environment. We do 
not call it intuitive, because we do not care to raise 
the question that the word intuition suggests, — a 
question with which we have no immediate concern. 
But whether the result of intuition or of inspiration, 
or, more probably, of both of these ideal functions of 
the mind, acting, as we have said before, under its 
environments, the conception is unquestionably as 
spontaneous as it is real. 

In discussing the development of the fundamental 
conceptions of all religions, it is not necessary for us 



10 THE ARGUMENT OF NATURAL THEOLOGY. 

to enter upon any abstruse questions of ethnology, 
archaeology, or philology, although all this learning 
might be brought to bear on the subject. The gen- 
eral conclusions with which alone we shall have to 
deal, are so patent that they will be accepted by 
every one, and this circumstance alone shows how 
fundamental are the phenomena we are considering. 

When the child first becomes conscious of his free 
will he finds that will opposed by other wills like his 
own, and we all know what an essential condition 
of education is the conflict which results. In our 
short-sightedness how greatly do we regret this con- 
flict, how earnestly seek to avoid it, and how often 
do we shun the responsibility it involves; and yet 
how fully do we recognize that no strength of char- 
acter, no force of will, no power of Intellect, no assur- 
ance of faith, can be gained except by conflict; how 
often only after repeated disasters are these virtues 
secured, and how forcibly does some of the most 
beautiful imagery of our language illustrate this 
truth. 

As to every child, so with freedom of the will 
there must have come at some first time to primeval 
man the conception of an opposing will; and the 
warfare then began through which the race has been 
educated. Admit that this conflict is but a continu- 
ation of the struggle for existence which began with 
life, yet now certainly the struggle involves for the 
first time conscious personality, and the mysterious 
knowledge of good and evil, so inseparably associ- 
ated with that freedom which makes us responsible 
beings. 



THE ARGUMENT OF MIGHT. II 

Through the conflicts of his will man acquired 
his first conception of power, the earliest measure 
of his own strength. In his fellow-men he at once 
recognized powers commensurate with his own, to 
which he was frequently forced to yield, but which 
he could often overcome ; and with such powers he 
from the first associated personality. But it required 
only a short experience with nature to force upon 
him the knowledge that he was under the control of 
powers vastly superior to those of men, which he 
could not withstand, and by which his fellows were 
frequently overwhelmed, — powers so mighty and so 
hidden that he quailed and trembled before them. 
As he knew power only as an attribute of personality, 
he ascribed the powers of nature to mighty and 
exalted personages capable of such vast effects ; and 
hence came man's first conception of God. The God 
thus conceived was merely the God of might, the 
God who rules in the tempest and directs the thun- 
derbolts, the God who rejoices in war and carnage. 
Moreover, these powers did not seem to be wielded by 
a single person. Man was still far from the concep- 
tion of a Jehovah ; but as he was opposed by many 
persons so his fancy filled the heavens with a host of 
warring gods. 

It is not our purpose to sketch the numberless 
fanciful forms which under different associations the 
early conception assumed. We desire only to em- 
phasize the fact that the earliest conception of God 
was that of a God of Might, and that this conception 
came to the savage as an obvious suggestion of na- 
ture. It was an induction from observed facts ; and 



12 THE ARGUMENT OF NATURAL THEOLOGY. 

simple and obvious as the induction was, the mental 
process by which it was reached differed in degree 
only, not in kind, from the inductions of modern 
science. 

Such inductions do not of course bring with them 
their credentials ; but in so far as they embody truth, 
they become accredited through experience, and 
chiefly in two ways : first, by their universality, that 
is, by coming to many persons independently, thus 
showing that they are in harmony with the constitu- 
tion of the human mind ; and secondly, by their 
permanency in retaining their hold on men, indicat- 
ing that they have stood the test to which they have 
been exposed, and by which they have been tried. 

The primitive inductions of men must necessarily 
be very partial truths, and the grain of truth is con- 
stantly so incrusted with error that it is with difficulty 
discovered; but I feel persuaded that beliefs which 
are long held in reverence owe their power to this 
grain of truth, however small. 

A most striking feature of inductions, by which 
they are plainly distinguished from deductions, is to 
be found in that inductions are progressive, and 
become clarified with experience. A deduction is 
demonstrative, and if the premises are correct, the 
conclusion naturally follows. There is no question 
as to degree, no room for doubt except as regards 
the premises of the argument. An induction, how- 
ever, may have every possible degree of certitude, 
from an unverified conjecture to a law of nature con- 
firmed by experience. Moreover, in the progress of 
knowledge it has been constantly the case that the 



INDUCTIONS BECOME SLOWLY CLARIFIED. 1 3 

conjecture has appeared as a law only after a slow 
clarifying process. As the dregs have settled from 
the intellectual medium, the truth has been seen in 
ever clearer outHnes; its essential features have be- 
come evident, while the grosser aspects of the orig- 
inal crude conception have disappeared. Such has 
been the uniform history of the great generahzations 
of science, and through such a clarifying process are 
most, if not all, of them still passing. Possibly in 
a very few cases the truth even now appears in all 
its simplicity ; but there can be no question that in 
the case of most of the fundamental principles of 
modern science of which we feel so proud, and which 
have been such valuable guides in the study of na- 
ture, the truths they embody are still only seen as 
in a glass darkly. It has been the privilege of a few 
gifted minds to see the truth of the inductions they 
have made generally recognized during their life on 
earth, but as a rule so many minds have concurred in 
developing these general truths that they must be re- 
garded as the product of the age, rather than as the 
gift of any one man to the knowledge of the world. 

These features of scientific generalizations are strik- 
ingly characteristic of the fundamental religious con- 
ception, which is also, as we have claimed, an induc- 
tion from observed facts. As first seen through the 
mists of barbarism, God was a Moloch, or a Thor, or 
at best a Jupiter ; but as in proportion to his men- 
tal growth man's spiritual vision became clearer, the 
image became ever more definite, more beautiful, 
and more lovely. It is not our purpose to trace 
the connection between the thousands of fantastic 



14 THE ARGUMENT OF NATURAL THEOLOGY. 

shapes which the first crude shadowy form assumed, 
in the history of different peoples, but we must mark 
four important stages of the conception, that are asso- 
ciated with different phases of the argument of nat- 
ural theology. 

It was a very important, although doubtless a very 
early advance in the progress of our race, when men 
first invented weapons and tools, in order to apply 
their brute strength more effectively, or direct it to 
more useful ends. By the use of tools primeval man 
was most markedly distinguished from all the ani- 
mals with which he was associated, including the 
highest anthropoids, from some of whose progenitors 
man is supposed to have descended. 

No one has claimed that even the rudest tools were 
ever made by anthropoids, however close their re- 
semblance to man ; and the appearance of stone im- 
plements in the strata marks the introduction of man 
upon the earth with remarkable sharpness. There 
seems to be here a most striking break of continuity, 
which the doctrine of gradual evolution has not hith- 
erto explained. The bones which we invariably find 
with these rude tools are those of well developed 
men, oftentimes with skulls at least as capacious as 
our own. 

However the evolutionists may explain these note- 
worthy facts, there can be no question that tools, 
even in their most primitive form, are proofs of a de- 
gree of intelligence which did not appear on earth 
until, outwardly at least, man had become essentially 
the same creature that he is to-day. In proportion 
as man has risen in the scale of intelligence he has 



INTELLIGENT USE. 1 5 

displayed an ever increasing ingenuity in the inven- 
tion of tools ; and the printing-press, the power-loom, 
the steam-engine, the electric telegraph, are the tools 
of our civilization, as the flint arrow-heads and stone 
axes were those of primeval man. 

Obviously, all tools or other implements are evi- 
dences of intelligence. If now we inquire on what 
basis this evidence rests, I think it will be found to 
depend on the fitness of these implements for an in- 
telligent use. We use the word *' implements " here 
in the broadest sense, for any utensils, even orna- 
ments, wrought for a specific use ; and it is the fitness 
of such implements for an intelligent use which consti- 
tutes the evidence of intelligence that such objects as 
are collected in an archaeological museum afford. - It 
may be that the archaeologist cannot determine the use 
of certain objects, but even such objects bear marks 
of having been wrought with tools, whose intelligent 
use is known, and must therefore be classed with 
them. In the last analysis intelligent use is the funda- 
mental evidence on which our conclusion as regards 
the intelligence of the agency which fashioned the im- 
plements depends ; and the fitness of the implements 
for such use, or even the traces of tools having such 
fitness, are a secondary but still a conclusive evidence, 
of intelligence; because such fitness, or traces, dis- 
tinctly point out the intelligent use for which the 
implements were made. It is not the marks of the in- 
scription which are the fundamental evidence of the 
intelligence that an inscription always suggests, but 
the thought which these marks have often concealed. 
Before the Assyrian characters could be read it was 



1 6 THE ARGUMENT OF NATURAL THEOLOGY. 

not seriously doubted that they were the writings of 
men, because they bore a close resemblance to such 
writings. But evidently if the arrow-head characters 
had proved to be simply the effect of natural causes, 
like the crystal outlines on a slab of graphic granite, 
such markings would be no longer any evidence of 
intelligence. On the other hand, if they had proved 
to be simple ornamentations they would still be evi- 
dences of intelligence; and, even if it had only ap- 
peared that they had been cut or moulded with tools, 
however rude, they would likewise be evidences of 
intelligence through the intelligent use of the tools 
employed. 

In discussing this question we cannot be too care- 
ful constantly to bear in mind that it is the intelligent 
use of tools which is the evidence of intelligence ; and 
that the fitness of the tools is also a proof of intelli- 
gence only so far as it clearly indicates an intelligent 
use. It is not necessary in this connection to distin- 
guish the fabrication of a tool from its use ; for the 
fabrication implies the use, and also the use of other 
tools, from the most complex down to the simplest 
tools furnished by nature, — a bamboo from the 
thicket, a stalk of flax from the field, or a sharp stone 
from the brook. It may often be that a tool will be 
found better adapted for some other use than for the 
one for which it was originally made, when its use in 
the new relation will be just as much an evidence of 
intelligence as its first use. 

Every one has heard the story of Timothy Dexter, 
who, in his absurd, and probably not very truthful, 
personal narrative, says he made a successful venture 



INTELLIGENT USE. 1/ 

by sending a cargo of warming-pans to the West 
Indies, where they were found to be admirably fitted 
for the purpose of straining sugar. Evidently the use 
of the pan for straining sugar was as much an evi- 
dence of intelligence as its use as a warming-pan ; 
but the fitness of the tool for either purpose was of 
value as evidence only so far as it indicated an intel- 
ligent use. The warming-pan, however admirably 
adapted for the purpose, was not designed for strain- 
ing sugar; and the illustration, whether authentic or 
not, plainly shows that in human relations fitness 
proves design, that is, intelligence, only so far as it 
indicates intelligent use. In the relations of an infin- 
ite being who knows all the ends from the beginning 
it is doubtless otherwise ; but this we cannot assume 
in our argument from design, and the failure to make 
the distinction we have drawn has often exposed this 
argument to undeserved contempt. 

Another anecdote illustrating the same distinction 
has the advantage of being certainly true. A West 
India planter sent to his overseer from New York a 
number of wheelbarrows, by whose use he expected 
to economize labor on his plantation. They were 
duly received, and the overseer wrote that they had 
been found to be very useful ; but what was the plant- 
er's surprise on returning home, to see the negroes, 
after shovelling in the earth, lift the barrows on to 
their heads and march off with the load in their old 
accustomed way. One can easily see that, compared 
with the wicker basket previously used, the wheel- 
barrows, even thus handled, might prove a saving of 
labor, and can recognize a low intelligence in the 



1 8 THE ARGUMENT OF NATURAL THEOLOGY. 

negroes who accommodated the new tool to their old 
habits. But if they ever thought at all, those negroes 
must have been puzzled by the wheel, and it must have 
presented to them a problem of very much the same 
kind that the much discussed rudimentary organs 
offer to the modern teleologist. Certainly, the wheel- 
barrow was not designed to be carried on the head, 
and the neglected wheel was the constant witness of 
this fact ; but the ultimate evidence of intelligence in 
the wheelbarrow was not in its fitness for one use or 
for the other, but in the use itself which the fitness 
indicated. The fitness is important solely as testify- 
ing to the intelligent use. 

Our early ancestors, however, were not troubled by 
the analysis of any such distinctions as those to which 
we resort, to justify their usually correct conclusions, 
however much they may have erred in special cases. 
They associated an intelligent personality directly 
with fitness, wherever found. As nature offers num- 
berless examples of fitness vastly more wonderful than 
that displayed by any human tools, they ascribed all 
such relations in the scheme of nature to the wise de- 
signs of the gods whom they already recognized as 
wielding the powers of the world. From the brain 
of Jupiter came Minerva with her loom, and Vulcan, 
with his forge ; and from such beginnings the argu- 
ment from design has been handed down to our day. 
And so closely have men always associated fitness with 
personal intelligence that in all languages the words 
expressing these relations have acquired such a color- 
ing that when we use them in connection with teleo- 
logical arguments we appear to beg the question in 



FITNESS IN NATURE. 1 9 

the simple statement of the case. Such words as " de- 
sign," "contrivance," and ''adaptation," all imply a 
personal agent; and in looking for a word which 
would express simply the external relation from 
which the inference of personal agency is drawn we 
could find no other than the one which we have so 
continually used, namely, fitness. Largely in conse- 
quence of the misuse of terms the argument from 
design has in recent years fallen into such disfavor 
that the very word, ** teleology," carries with it a sug- 
gestion of opprobrium ; and yet the argument is in- 
trenched as strongly as ever behind defences which 
have always been assaulted in vain; but let us be 
sure that we fully know where the strength of our 
position lies. 

It is not true that fitness in nature in any limited 
relations is satisfactory evidence of design, and the 
easy " reductio ad absurdum " with which such an 
assumption is readily met has done not a little to bring 
teleology into contempt. As has been shown, this 
assumption is not true even in human relations. With 
the tools of men it is not their fitness for certain uses 
but the intelligent use which is the real evidence of an 
intelligent mind ; and far less in nature can we claim 
to know the purposes of the Original ; and if we at- 
tempt to enforce our argument by the plea that there 
can be no use which Omniscience could not have fore- 
seen, as before intimated we directly assume the very 
point we are attempting to prove. Nevertheless the 
premises of our argument are unquestioned; and 
these are the relations of fitness in nature, wonderful 
beyond language to express, intricate beyond thought 



20 THE ARGUMENT OF NATURAL THEOLOGY. 

to unravel, sublime beyond imagination to conceive, 
useful beyond words to admire. Now men have been 
able to discover but one satisfactory explanation of 
these relations, namely, that they are the outcome of 
an intelligence like their own, only of an immeasur- 
ably higher order, — in a word, that they were created 
by the Jehovah of the Bible. We must not claim 
that we have here logical proof, for we cannot have 
any such demonstration. But we have something 
which is far better than all logical proof, something 
which, while it carries conviction, inflames our imagi- 
nation, and appeals to our faith. We have what we 
technically call an induction. But it is an induction 
of the highest order, with material so ample and ex- 
perience so extended as to leave no room for reason- 
able doubt. 

In claiming for an induction the validity of a de- 
ductive demonstration, we compromise the whole 
strength of our logical position; and hence many 
writers on natural theology, even though they may 
not have attempted to analyze the argument from de- 
sign, have discussed the examples of fitness in nature 
as illustrations of an admitted principle, and not as 
proofs of an intelligent author. In the book before 
referred to, we ourselves have most distinctly and 
emphatically maintained this attitude towards the 
subject. It must be remembered, moreover, that on 
this view and for the argument's sake such discussions 
are perfectly legitimate ; for the conviction which an 
induction produces depends chiefly on the extent of 
the field which it grasps; and when we study this 
great induction of natural theology how wonder- 



THE ARGUMENT FROM SKILL. 21 

fully da we find that it has borne the tests both of 
universality and of experience. Not only is it an in- 
duction which omits no known fact, but it is an induc- 
tion of all people, in all ages, and under all conditions. 
How unmoved also has it borne the test of experi- 
ence. Every attempt has been made to set it aside 
by showing how this universe might have issued 
without an intelligent Creator, — from the time of 
the " fortuitous concourse of atoms " of Lucretius 
to the ** struggle for life " of Darwin. But although 
by stimulating thought and inciting deeper study 
these attempts have profoundly modified and en- 
larged man's earlier crude conceptions of the Divine 
methods, they have always resulted at last in impress- 
ing the great mass of thinking men with a deeper con- 
viction of His being, with a grander conception of His 
power, and with a more profound reverence for His 
skill, who is the Alpha and Omega of all knowledge, 
the Beginning and End of all life. 

Beauty is simply that harmony of proportions and 
qualities which results from the most complete fitness 
of all the parts in a perfect whole ; and in the educa- 
tion of mankind the worship of skill naturally grew 
into the worship of beauty, or rather of that material 
perfection which is manifested in beauty. Early in the 
history of civilization the culture of beauty reached 
its highest development in ancient Greece ; and then 
appeared another phase of the argument of natural 
theology, which, for the sake of distinguishing the 
stages in the development of the subject, we may call 
the argument from beauty, although it does not differ 
essentially from the argument from design. As before, 



22 THE ARGUMENT FROM BEAUTY. 

the argument is solely an induction. We have for 
the premises the infinite beauty of nature, and for the 
induction the inference that all this beauty must have 
issued from a Personal Being vastly more susceptible 
than any human nature to the harmonies of form, of 
color, and of sound. 

This argument, although not recognized as such, 
has a singular attraction to a well marked class in 
modern society, who, having revolted from the pre- 
vailing creeds, seek satisfaction for their minds and 
hearts in the contemplation of all that is most perfect 
in art ; and this argument strongly appeals to a vivid 
imagination and a cultivated taste. These worship- 
pers of the beautiful hold in highest honor the pro- 
ducts of Greek art which have come down to us, and 
often even look back with regret to that old civiliza- 
tion as the highest stage ever reached in the intellec- 
tual development of man. But Greek beauty was 
simply a material beauty, and the God which the 
Greek apprehended was simply a perfect sensuous 
being, capable of realizing in his person and his cre- 
ation the most perfect harmonies, but also revelling 
in the sensuality with which, before Christianity, ma- 
terial beauty was always associated. Lifted into a 
more spiritual sphere, and protected by the safe- 
guards of Christian morality, the modern devotees of 
art may disassociate material beauty from such gross 
accompaniments ; but who that has known human 
nature in its lower moods can for a moment question 
that the vilest orgies would again become rife if the 
religious convictions by which alone our Christian 
civiHzation is maintained were undermined? 



THE ARGUMENT FROM LAW. 2$ 

As the Greek passed under the Roman sway, so 
did the supremacy of beauty yield to the supremacy 
of law ; and this was a natural and an intellectual pro- 
gress. Beauty, as we have seen, is the harmony of 
relations which perfect fitness produces ; but law is 
the prevailing principle which underlies that har- 
mony, and without which no harmony can be main- 
tained. In the ancient world Greece appeared as the 
representative of beauty, and Rome succeeded as 
the expositor of law. In the fluctuations of nature 
the material forms of beauty are transient, and unless 
constantly reproduced under the operations of per- 
manent laws can have no lasting influence. In Greece 
the productiveness of art soon ceased, through failure 
of the authority of law to restrain her civil dissen- 
sions, and the power of beauty to mould men lay 
dormant until Christianity had wrought its work, and 
the genius of beauty became wedded to the spirit of 
the new religion. On the other hand, the fundamental 
principles of law are eternal, and Rome, through her 
civil law, has never ceased to rule the world. 

It was a very long step in the progress of mankind 
from the promulgation of the civil law of Rome to 
the recognition of the laws of nature, — from Justinian 
to Newton; and since the discovery of the law of 
gravitation so slowly has this conception pervaded 
the popular mind that not until our own day have 
even cultivated men fully realized that their race has 
been educated under a reign of law, which embraces 
the universe, and which began with time, — a system 
of laws of which the best of human codes offers only 
a feeble type. 
3 



24 THE ARGUMENT OF NATURAL THEOLOGY. 

The study of natural laws has brought fresh evi- 
dence to the support of the conclusions of natural 
theology, and evidence of the most impressive kind. 
These laws are at once so grand and yet so simple, 
so high and yet so near, so universal and yet so par- 
ticular, so far reaching and yet so present, so invari- 
able and yet so beneficent, that while they tax to the 
utmost his intellectual power, they are calculated to 
impress the mind of the student with awe, with rever- 
ence, and with trust. Newton has described the im- 
pression which the discovery of the law of gravitation 
made on him, and many of the great masters of 
science join to his their united testimony that the 
study of the laws of nature has wrought the most 
profound conviction of the presence of an overruling 
Mind. The devout student of science finds it difficult 
to conceive how it could be otherwise, and simply 
wonders at the perversion of the intellectual vision to 
which the heaviness of the flesh or the subtleties of 
the brain may sometimes lead. 

The phase of the argument of natural theology 
which is based on the laws of nature, we have called 
in another place the argument from general plan; 
although, like the argument from beauty, it is not 
essentially different from the argument from design. 
The writer to whom we have before referred regards 
the argument from general plan as the only legiti- 
mate form of the argument from design, and urges 
that while we cannot prove that fitness may not have 
resulted from natural selection, or from some other 
undefined principle of nature, order must always be a 
product of intelligence. But, obviously, — as long ago 



LAW IMPLIES A LAWGIVER. 25 

Spinoza so powerfully argued, — order, or law, may 
be merely a subjective attitude or posture of our own 
minds towards external nature ; and the words *' law," 
"order," "plan," imply personal intelligence as plainly 
as do the words "design," *' contrivance" and ** adapta- 
tion" before discussed. To say that law implies a law- 
giver is just as much a begging of the question as to 
say that design implies a designer. The truth simply is 
that this last phase of the argument of natural theol- 
ogy, like all the other phases, is an induction, and not a 
necessary deduction. Of this induction the premises 
are the invariable relations of natural phenomena; 
and the inference is that these fixed relations must 
have been determined by a Supreme Intelligence, 
who ordained the order and law of which the universe 
is the expression. Christian students are most firmly 
persuaded that this conclusion is the only reasonable 
or intelligible explanation of the facts, and the wider 
our knowledge becomes, the more fully is their con- 
viction confirmed. But it is easy to cavil, — that 
the observed constancy of relations may have been 
caused by some undefinable potency of material 
things (the law of philotaxis, for example, resulting 
from a tendency in the leaves of a plant to expose 
the most surface to the sun), and then the whole 
matter is summed up with the scoffing remark of 
Voltaire, ** The heavens only declare the glory of the 
astronomers," who see their own intelligence reflected 
in the circling orbs. If we would protect our sacred 
cause from such sneers, we must be careful to estab- 
lish it in truth, and not claim for it a sanction which 
it does not, and never can possess. 



26 THE ARGUMENT OF NATURAL THEOLOGY. 

We have now passed in rapid review four phases 
of the argument of natural theology, corresponding 
to four stages in human development, — namely, the 
argument from might, the argument from design, the 
argument from beauty, and the argument from gen- 
eral plan. Corresponding to the recognition in na- 
ture of energy, fitness, beauty, and order, we have 
the inferences that might, skill, perfection, and law 
are the attributes of an Intelligence which created 
and sustains the whole. Here the scheme of natural 
theology ordinarily ends ; but, as it seems to us, the 
culminating phase of the argument, corresponding to 
the highest phase of human development, still re- 
mains to be stated. 

The doctrines of Christianity as a system of re- 
vealed religion do not of course come under our 
consideration ; but the facts of Christianity as histor- 
ical verities are as much subjects of natural theology 
as any other natural phenomena. The movements 
of history are phenomena of nature as well as the 
movements of the planets ; and considering the ad- 
mitted facts of our holy religion from this point of 
view, what a broad basis for induction do they fur- 
nish ! Indeed, the basis is so ample that we may at 
once waive everything that any sceptic will question. 
We may admit that all the miraculous features of the 
narrative are myths, and that the Bible has no more 
authority than the plays of Shakspeare, or any other 
book that portrays character. Still, after all conces- 
sions, there remains the character of Jesus, the reve- 
lation of perfect holiness, the exemplar of the noblest 
self-sacrifice, the manifestation of the purest love. 



THE ARGUMENT AN INDUCTION. 2/ 

Admit that the same traits have in some degree 
appeared in the founders of other religions, and even 
in classical literature, as they have in thousands of 
humble Christian lives ever since. Still, there re- 
mains the wonderful fact that this one character 
has transformed the world, and led to incompar- 
ably the highest and the purest civilization which 
the race has known. From these premises there never 
has been but one inference which has satisfied the 
mass of mankind who have come to the full knowl- 
edge of the facts, — the conclusion of that great apostle 
who, himself overpowered by the force of the evi- 
dence, declared that ** God was in Christ reconciling 
the world unto himself." 

Here as in every other previous phase of our argu- 
ment we have simply an induction; not a demonstra- 
tion, but an induction which has produced conviction 
in a multitude which no man can number; which has 
satisfied the deepest yearnings of humanity; which 
has given superhuman courage to martyrs, and sus- 
tained the unwavering devotion of saints. It is an 
induction, moreover, which has always stood the test 
of experience under every circumstance of life ; and 
among its confessors have been all sorts and condi- 
tions of men, from the humblest intellect to the most 
gifted genius. It is never outgrown, but its power 
increases as men grow in wisdom and in virtue. It 
is an induction which opens ever fresh fields of spir- 
itual knowlege, and directs in the way of truth. In 
a word, as it is the noblest induction that man has 
ever grasped, it is also the greatest power in the 
world. 



2S THE ARGUMENT FROM LOVE. 

We thus lay hold of the last phase of the argument 
of natural theology ; and this we may call the argu- 
ment from love. At the same time we reach the 
highest stage in the development of man's concep- 
tion of God. How gradual but how majestic has 
been the progress in the education of mankind from 
the first ! How large the result ! In nature man found 
Energy, Fitness, Beauty, Order, and Sacrifice; and 
through these he has been led to recognize Might, 
Skill, Perfection, Law, and Love, in a Supreme Intelli- 
gence. The argument, however its materials may 
differ, is in spirit one throughout all its varied phases ; 
and the one point we would impress is that this argu- 
ment is an induction. To show the validity of the 
argument by comparing the inductions of natural 
theology with the inductions of science will be the 
object of these lectures. 



INDUCTION AS DEFINED BY ARISTOTLE. 29 



LECTURE II. 

PREPARING THE WAY. 

IN the first lecture, when drawing the distinction 
between inductive cognition and deductive dem- 
onstration, we used the word " induction " in the fa- 
miHar sense in which it is usually employed among 
physicists, to include the numerous phases of the 
experimental method of discovering general truths, 
without overlooking the fact that the logicians have 
generally given to the same term a more precise and 
definite meaning. In its Greek form the word " induc- 
tion " is as old as Aristotle, who gives a formal anal- 
ysis of this mode of reasoning, which is not more 
obscure than a similar philosophical analysis of so 
complex a mental process might be at the present 
day. 

Certainly the great Stagirite had grasped the essen- 
tial distinction between induction and deduction when 
he wrote : " Induction makes clear only, and does 
not prove." And although he confuses his modern 
reader when he discusses induction as a proof which 
may be formulated in a syllogism, he elsewhere 
clearly recognizes this mode of reasoning as a kind 
of inference through which we arrive at general prin- 



30 INDUCTION AS DEFINED BY BACON. 

ciples. A more precise definition of the mental part 
of the process could not now be given. 

Bacon, who is regarded by English scholars as the 
father of the inductive method, held a more mechan- 
ical view of the subject. In nature general truths are 
constantly obscured through the complexity of the 
data furnished by experience ; and Bacon proposed 
to sift them out, as it were, by a perfectly definite 
method of exclusion or elimination. We seek the 
cause of a certain class of effects ; say, for example, 
of motion in circular orbits. Bacon would make a 
critical comparison of all cases in which the effect is 
produced until by exclusion of one after another of 
the various circumstances he is able to detect some 
phenomenon constantly present when the effect is 
present, and varying in degree with the effect, and 
without which the effect is never produced; when 
this phenomenon — if one lived long enough to 
distinguish it — must be a cause of the effect in 
question. Obviously, an exhaustive elimination of 
conditions is rarely possible; and this Bacon recog- 
nizes, and gives rules for procedure in various cases 
and recommends various aids to induction, — *' ad- 
mincula " as he calls them, — by which the process 
may be greatly expedited. 

Bacon's method was the normal outcome of his 
metaphysics, — that is, of his a priori conception of 
nature and of natural processes, — and as the con- 
ception was very partial the method was necessarily, 
even in theory, equally limited. Practically no great 
originator in science ever followed Bacon's rules, or 
any other rules; although under the circumscribed 



bacon's influence. 31 

conditions of ordinary experimental work every phys- 
ical investigator naturally resorts to a method of 
elimination in seeking the cause of any accidental 
disturbance, such as a leak in his apparatus, or a 
break in his electrical connections. 

It is a singular fact that Bacon, who is usually re- 
garded among English-speaking people as the cham- 
pion who freed the human mind from servitude to a 
priori dogmas, should himself have been so greatly 
influenced by his metaphysics. Bacon constantly set 
induction in opposition to deduction, and regarded 
syllogism as of service only for the communication of 
knowledge. But, obviously, wherever the universal 
can be connected with the particular the process of 
thought can be expressed in a syllogism; and if 
Bacon could have succeeded in realizing his meta- 
physical conception he would have also succeeded 
in placing induction on the same basis as deduction, 
and rendered the method equally demonstrative. 

It is also a current opinion that Bacon was the first 
to make the results of observation and experiment 
essential factors in scientific reasoning. But this, 
again, is only partially true. Aristotle constantly 
appealed to the facts of nature in support of his con- 
clusions, and there are at least hints in his writings of 
experimental methods; and in classical writings of 
a later date we have abundant evidence of accurate, 
discriminating, and intelligent observations. As com- 
pared with Aristotle, the greater influence of Bacon 
on the advancement of knowledge is not to be found 
so much in the superiority of his methods as in the 
larger knowledge of nature and the clearer scientific 



32 BACON DID NOT INVENT "INDUCTION." 

conceptions among the men whom he influenced ; 
and it is safe to say that if the " Novum Organum " 
had been given to the world a few centuries earlier 
it would have led to no greater results than those 
produced by the far older ** Organon " which it 
superseded. 

One influence of Bacon's great genius has been to 
spread very widely the narrow meaning which he ap- 
propriated for the word " induction." Indeed, accord- 
ing to a common popular misapprehension, Bacon 
invented the word, as well as the mechanical method 
which it is often used to indicate. But, as has been 
intimated, this word, or its equivalent in different 
languages, has been in constant use from the time of 
Aristotle ; and was employed by the Stagirite with a 
far more comprehensive and deeper meaning than 
was ever conceived by King James's at once great 
and contemptible chancellor. We now use the term 
in a far broader sense than ever before ; but so far as 
the prehminary mental act is concerned, our concep- 
tion of the process of induction does not differ ma- 
terially from that of Aristotle. Its essential features 
are, first, the conception or guess ; secondly, the 
verification of this conception by experiment and 
observation. The verification may be direct, or 
through some more or less remote deduction ; and if 
the appeal to nature shows that the first conception 
must be rejected, the experience will probably sug- 
gest some modification which will be tested in like 
manner in its turn, until the truth in more or less 
completeness is reached. 

This system of observation and experiment, con- 



BASIS OF SUCCESSFUL INDUCTION. 33 

tinued during a long period of time, has given to the 
modern worid a far more intimate acquaintance with 
natural phenomena than the ancients possessed ; and 
it is to this, and not to superior philosophy, that our 
great success in the advancement of knowledge is 
to be attributed. 

You pronounce with confidence on the probability 
of a friend's action in a given case in measure as you 
are acquainted with his principles and inclinations. 
In a very similar way the investigator who is ac7 
quainted with nature and her processes is likely to 
make inferences, which will be confirmed by experi- 
ence in just the proportion that his knowledge is 
wider and more exact. The ancients were often as 
ingenious and as profound in their conceptions 
as modern philosophers, and their anticipations of 
knowledge surprise us. But as their conceptions 
remained unverified, they laid no sure foundations 
on which they could build. Because wild and scat- 
tered, all their ingenuity was misdirected and unavail- 
ing. The value of a man's guess depended on his 
reputation; and questions of fact were settled on 
authority. Thus it came to pass that Aristotle's 
unverified conjectures, through the sheer force of his 
intellectual pre-eminence, misled the world for two 
thousand years. 

Besides his more intimate acquaintance with na- 
ture, the modern student is constantly acquiring im- 
proved methods of testing his inferences ; and such 
instruments as the telescope, the microscope, the 
polariscope, the spectroscope, the thermometer, the 
galvanometer, and the telephone have not only im- 



34 PREPARING THE WAY. 

mensely widened his field of observation, but also 
vastly increased his power of experimenting ; so that 
his progress in knowledge has been so constantly 
and so rapidly accelerated that more has been 
gained during the lifetime of men still living than 
during all human history before. 

As our object in these lectures is to show that the 
inductions of natural theology are as legitimate as the 
inductions of physical science, it is essential that we 
should first describe the characteristics of scientific 
inductions, in the broad sense with which we use this 
term ; and since, as we have endeavored to show, it 
is impossible to define this mode of reasoning by any 
concise formula, we shall best attain our object by 
studying a few striking examples, — selecting for ex- 
amination great discoveries whose history is well 
known, and of which the important steps can readily 
be traced. Let us begin, however, with a brief de- 
scription of some of the speculations of the old 
Greek philosophers, in order that by comparison we 
may more fully appreciate the value of our modern 
inductive methods. 

It will be remembered that the Father of History, 
when seeking to explain the cause of the annual in- 
undations of the Nile, — after giving his reasons with 
a truly scientific spirit (if sometimes with insufiicieht 
knowledge) for rejecting the hypotheses which had 
been proposed to him, — proceeds to argue that the 
effect is caused by the sun, which unequally draws 
the water from the sources of the stream at difi"erent 
seasons of the year; and that the overflow takes 
place when the sun has gone north, and draws less 



ILLUSTRATION FROM HERODOTUS. 35 

powerfully on the Libyan fountains, which then pour 
out their full supply. 

Assuming the sufficiency of the alleged cause, the 
explanation of Herodotus is still confused ; but what, 
as it seems to me, he distinctly implies is this : The 
Nile is unique among rivers, first, because it flows 
from the south to the north, across the region twice 
traversed by the sun in the course of the seasons ; 
and secondly, because, having no tributaries, it is not 
affected by the rains along its banks. Hence the 
alternations of its floods must depend on its sources 
alone; and the sun-god must produce the greatest 
possible difference of effect on these springs when 
at the extreme limits of his annual journey. 

Were the cause adequate this explanation certainly 
would not be unphilosophical; but all turns on this 
one point. Herodotus does not appear to have had 
any doubts about the adequacy of the sun's agency, 
or to have made any attempts to estimate the magni- 
tude of the effect which could thus be produced. 
His whole theory was expressed by the phrase, *' he 
(the sun) draws the water to him," — a form of 
words which has been used to describe a certain fa- 
miliar appearance in the heavens from that day until 
this. In using this expression — with which his read- 
ers at once associated the optical phenomenon just 
referred to, and which they connected in an obscure 
way with the evaporation of water — Herodotus felt 
that he was giving a triumphant explanation ; and 
this example shows in a marked way the reason of 
the unsoundness of the Greek philosophy when 
applied to the study of nature. The old Greeks had 



36 PREPARING THE WAY. 

as vivid imaginations, and were as acute reasoners as 
ourselves ; they were also in many cases diligent 
and careful observers. But they mistook abstract con- 
ceptions for realities; and having given names to 
these forms of thought, they sought to advance 
knowledge by analyzing the words and the thoughts 
suggested, instead of studying the facts which the 
words signify. 

This vicious method of Greek philosophy is well 
described by Whewell in his ** History of the Induc- 
tive Sciences : " " As soon as they had introduced 
into their philosophy any abstract and general con- 
ceptions, they proceeded to scrutinize these by the 
internal light of the mind alone, without any longer 
looking abroad into the world of sense. They took 
for granted that philosophy must result from the re- 
lations of those notions which are involved in the 
common use of language, and they proceeded to 
seek their philosophical doctrines by studying such 
notions. They ought to have reformed and fixed 
their usual conceptions by observation; they only 
analyzed and expanded them by reflection. They 
ought to have sought by trial, among the notions 
which passed through their minds, some one which 
admitted of exact application to facts ; they selected 
arbitrarily, and consequently erroneously, the notions 
according to which facts should be assembled and 
arranged. They ought to have collected clear fun- 
damental ideas from the world of things by induc- 
tive acts of thought; they only derived results by 
deduction from one or other of their familiar 
conceptions." 



SLAVERY TO LANGUAGE. 37 

But akhough the false method, thus so clearly de- 
scribed, was especially characteristic of the ancient 
philosophy, it is a vice from which the modern world 
has by no means wholly escaped. How often do the 
controversies of the present day turn on purely ver- 
bal distinctions. How imperiously, and yet often how 
insensibly, are our thoughts ruled by the mysterious 
mechanism of language. How conscious is the effort 
to force language to express our exact and deliberate 
thought, and to prevent our thought from being 
moulded by language. Of course to a very large 
extent the influence of language is legitimate. Lan- 
guage is the medium of thought, and cannot be sep- 
arated from it. Exact thought is not practicable 
without language, and the very effort to clothe thought 
in words awakens thought. Moreover, the general 
terms in language represent stages of intellectual 
progress. They form a scaffolding, as it were, by 
which the mind mounts to ever higher levels from 
which it gains a more general and wider prospect. 
But it is one thing to use language, and another thing 
to be a slave to it. Some men are slaves to language 
all their lives, and from such a slavery the ancient 
philosophy was not liberated until modern times. 

Man was made in the image of his Maker ; or, to 
express the same truth in the phraseology of a re- 
cent philosophy, has developed into harmony with 
his environment; and, undoubtedly for this reason, 
those acute thinkers of ancient time in their unveri- 
fied conceptions not unfrequently anticipated the 
results of modern science. So it was with Herodo- 
tus ; and, although he attached no definite meaning 



38 PREPARING THE WAY. 

to it, his explanation of the annual overflow of the 
Nile was in the main correct. The sun is indeed the 
cause ; and the great pump which the sun maintains 
in ceaseless action not only supplies the Nile, but 
also all the rivers of the globe. Moreover, such is 
the peculiar equatorial position of the basin of drain- 
age of this remarkable river that the evaporation 
from this area greatly diminishes as the sun moves 
north of the equator, when naturally an increased 
amount of water flows down the only other outlet. 

By the Greek philosophers the contrasts empha- 
sized by language were regarded as fundamental dis- 
tinctions in nature, or first principles, which they 
made the basis of discussion, and from which they 
sought to deduce general truths. Aristotle enumer- 
ates ten such principles, as based by the Pythag- 
oreans on the contrasts of number: limited and 
unlimited, odd and even, one and many, right and 
left, male and female, rest and motion, straight 
and curved, light and darkness, good and evil, square 
and oblong; and from oppositions of this kind Aris- 
totle himself deduced the doctrine of the four 
elements. 

" We seek," he says,^ " the principles of sensible 
things, — that is, of tangible bodies. We must take, 
therefore, not all the contrarieties of quality, but 
those only which have reference to the touch. Thus 
black and white, sweet and bitter, do not differ as 

1 As translated from De Gen. et Corrupt. : Whewell's His- 
tory of the Inductive Sciences, vol. i. page 49, edition of 1847 ; 
and the translations from Aristotle which follow are quoted 
from the same standard work. 



DOCTRINE OF THE FOUR ELEMENTS. 39 

tangible qualities, and therefore must be rejected from 
our consideration. Now the contrarieties of quality 
which refer to the touch are these : hot, cold ; dry, 
wet; heavy, Hght; hard, soft; unctuous, meagre; 
rough, smooth; dense, rare." Then, after rejecting 
all but the first four of these, either because they 
are not active and passive qualities, or because they 
are combinations of the four first, and concluding for 
these reasons that the four retained must be elements, 
he proceeds : — 

** Now in four things there are six combinations of 
two ; but the combinations of two opposites, as hot 
and cold, must be rejected. We have therefore four 
elementary combinations which agree with the four 
apparently elementary bodies; fire is hot and dry; 
air is hot and wet (for steam is air) ; water is cold 
and wet ; earth is cold and dry." 

In a similar way by considering light as opposite 
to heavy Aristotle came to regard levity as a quality 
of a body, and distinguished bodies as absolutely 
heavy or absolutely light. " Former writers " he 
says, "have considered heavy and light relatively 
only, — taking cases where both things have weight, 
but one is lighter than the other ; and they imagined 
that in this way they defined what was absolutely 
heavy and light." Fire and air, according to Aristotle, 
were absolutely light, with fire the lighter of the 
two. Hence it followed " that each of the four ele- 
ments tends to its own place, — fire being the highest, 
air the next, water the next, and earth the lowest." 
In another place he writes : " heavy and light are, as 
it were, the embers or sparks of motion ; " and he 
4 



40 SPECIFIC GRAVITY AND SPECIFIC LEVITY. 

considered that the tendency of light bodies to rise, 
like the tendency of heavy bodies to fall, was an in- 
herent quality. 

It is obvious that all this fallacious reasoning had a 
purely verbal origin; and that the great error con- 
sisted in inferring that there must be an opposition 
of material qualities corresponding to verbal distinc- 
tions. Since light was opposite to heavy, the con- 
clusion was drawn that levity, like weight, must be a 
quality of matter; and it was nearly two thousand 
years before men found out that levity, or buoy- 
ancy, — as we now call the upward tendency of tim- 
ber in the sea, or of flame and other forms of heated 
vapors in the atmosphere, — the phenomena out of 
which the Stagirite made so much, — was simply an 
effect of the weight of a surrounding fluid ; and we 
retain in our language the term specific gravity — 
originally opposed to specific levity — as a constant 
reminder of the persistency of error. Moreover, it is 
a striking illustration of the spirit with which the an- 
cient philosophy was cultivated, that this error pre- 
vailed in spite of the fact that Archimedes discovered 
and correctly enunciated the simple principle of buoy- 
ancy, — a discovery rendered most notable by its con- 
nection with the testing of King Hiero's crown. 

We must also briefly notice Aristotle's absurd con- 
clusions in regard to motion ; since they were gen- 
erally received even down to the period of the great 
astronomical inductions which we are next to con- 
sider, and without some knowledge of them we can- 
not comprehend the intellectual conditions under 
which the great astronomers of the sixteenth and 



MOTION AN INHERENT TENDENCY. 4 1 

seventeenth centuries studied and labored. Motion, 
according to the Stagirite, was simply the effect of 
the inherent tendency of the body. In consequence 
of their nature, light bodies move upwards and heavy 
bodies downwards; and, as was fully recognized, 
such motions acquire an ever increasing velocity. 
Since, then, acceleration was the characteristic of 
the motion of a body obeying its natural tendency, 
such motions were regarded as natural. On the 
other hand, when a ball is rolled along the ground 
the motion rapidly diminishes, and finally ceases, 
because the ball is forced against its inherent dis- 
position ; and hence, on the principle of oppositions, 
such retarded motions were distinguished as violent. 

This explanation, if it may be so called, of the 
motions of bodies remained almost unquestioned to 
the time of Galileo; and the results of his exper- 
iments were gravely questioned because they were 
inconsistent with the Aristotelian dogmas. But the 
climax of these unbridled dynamical speculations 
remains yet to be stated, and will form the turning- 
point in this discourse. 

In his book " On the Heavens" Aristotle wrote: 
" The simple elements must have simple motions ; 
and thus fire and air have their natural motions 
upward, and water and earth have their natural mo- 
tions downward. But besides these motions there 
is motion in a circle, which is unnatural to these ele- 
ments, but which is a more perfect motion than the 
other, because a circle is a perfect line, and a straight 
line is not; and there must be something to which 
this motion is natural. From this it is evident that 



42 THE QUINTA ESSENTIA. 

there is some essence of body different from those 
of the four elements, more divine than those and su- 
perior to them. If things which move in a circle 
move contrary to nature, it is marvellous, or rather 
absurd, that this, the unnatural motion, should alone 
be continuous and eternal ; for unnatural motions de- 
cay speedily. And so from all this we must collect 
that besides the four elements which we have here 
and about us, there is another removed far off, and 
the more excellent in proportion as it is more dis- 
tant from us." This fifth element was called the 
" quinta essentia " by Latin writers ; and the word 
" quintessence " in our own language frequently brings 
to mind this singular conception, which, although so 
absurd to us, held for ageaf a wonderful control over 
the human mind. 

Having thus shown how vain and foolish are the 
imaginations of men unless directed and controlled 
by experience, we turn next with satisfaction to a far 
more glorious record, and shall attempt to illustrate 
by a conspicuous example how this same noble and 
powerful imagination of man becomes like a divine 
inspiration if only he approaches nature with meek- 
ness, and strives to learn what she alone can teach. 
It is the disposition of the mind and the fulness of 
knowledge, more than method, more than skill, more 
than ingenuity, more than intellect, which makes the 
difference between foolish speculation and pregnant 
conception. 

The change from the ancient philosopher to the 
modern investigator is as great as the difference 
between the sophist and the scholar, between self- 



INFLUENCE OF CHRISTIANITY. 43 

assertion- and self-devotion, between conceit and hu- 
mility, between pretension and worship. This change 
of attitude of the students of nature since the revival 
of learning is often ascribed to the influence of Bacon. 
But great thinker as Bacon was, he did not lead the 
change, and knew httle of its true spirit. To explain 
such a wide-spread intellectual movement we must 
look to a more potent cause than the influence of 
any man, however great ; and, as it seems to me, this 
great revolution can be directly traced to the in- 
fluence of Christianity, and to the spirit of humility 
and self-devotion which its Founder sanctified and 
rendered glorious. 

The Law of Universal Gravitation, says Dr. Whewell, 
the historian of the inductive sciences^ *4s indisputa- 
bly and incomparably the greatest scientific discov- 
ery ever made, whether we look at the advance 
which it involved, the extent of the truth disclosed, 
or the fundamental and satisfactory nature of this 
truth." And although it may be doubted whether 
this discovery was as an intellectual achievement any 
greater than many others which have been made since, 
there can be no question that not one of these, how- 
ever brilliant, has had so great and lasting an eff"ect in 
the advancement of learning. Selecting, therefore, 
the law of gravitation as a most conspicuous example 
of a scientific induction, let us endeavor to follow, as 
far as is possible, the several steps by which the great 
result was achieved, in order that we may thus gain 
a clearer conception of the mental process, called in- 
duction, which v/e are seeking to illustrate. 

^ Whewell's History of the Inductive Sciences, vol. ii. p. 187. 



44 PRELUDE TO NEWTON. 

In order to understand what Newton accomplished, 
it is essential that by studying the state of knowledge 
at his time we should put ourselves in some measure 
in his position when, at the age of twenty-three, he 
received the degree of Bachelor of Arts at the Uni- 
versity of Cambridge. Thorough mathematical stu- 
dent of great ability that he was, we must suppose 
him versed in all the astronomical learning of the 
day ; but at the same time he must have been more 
or less hampered and prejudiced by the forms and doc- 
trines in which he had been educated, — limitations 
from which only men of genius are able to escape. 
On the other hand we must remember that besides 
the astronomical works which had been actually pub- 
lished and were then common property, Newton also 
had the advantage of a large amount of floating dis- 
cussion, which did not ripen into definite results until 
a later day, but which made Newton's grasp of the 
great ideas involved in his discovery a more natural 
and less transcendent effort than it would otherwise 
appear. 

Such historical relations as we would establish are, 
however, very difficult to secure ; for even if we can 
fully realize the conditions of actual knowledge in 
Newton's time we cannot appreciate those influences 
of education, surroundings, and other circumstances 
which so greatly modify the intellectual atmosphere 
in which men live and work, and by which facts and 
opinions are always more or less colored. Hence, it 
is impossible for any one at the present day, even 
after long continued study and investigation, to stand 
where Newton stood in his opening manhood, and 



THE ALMAGEST. 45 



view the field of knowle(5ge as he saw it ; and for me 
it is only practicable to sketch the situation in rudest 
outlines. 

The knowledge of astronomical facts acquired by 
the ancients was very extensive. From the time of 
the Chaldean shepherds there were always numerous 
and assiduous observers of celestial phenomena. In- 
deed, among eastern nations the heavenly hosts were 
so universally objects of worship, and the conjunc- 
tions of the planets were supposed to be so intimately 
connected with men's lives that astronomical occur- 
rences received an attention which no other phe- 
nomena of nature secured. As early as 150 B.C. 
Hipparchus constructed a system of astronomy which 
even now commands our admiration. We have a 
very full exposition of this system by Ptolemy, who 
lived under the Emperor Hadrian two hundred and 
fifty years later, and whose work has been preserved 
for us by the Arab astronomers under the title of "The 
Almagest." Ptolemy added but Httle to the theory of 
Hipparchus, but he did a great deal to extend and 
verify it. " The Almagest" is a monument to his learn- 
ing, accuracy, judgment, and skill ; and is by far the 
most important contribution to scientific knowledge 
which we have received from the ancient world. 

When we remember that the observations of the 
ancients were made with no aids, or with only the 
rudest tools, the knowledge of celestial phenomena 
which had been acquired at the time of Hippar- 
chus appears wonderful. The fixity of the stars had 
been established. The brighter stars had not only 
been grouped in constellations and mapped, but their 



46 ASTRONOMY OF THE ANCIENTS. 

relative positions had been determined, by alignments, 
with such accuracy that the observations are of value 
at the present day. The paths of the planets and of 
the moon — and what is still more remarkable, the 
course of the sun through the constellations — had 
been followed, and the varying rapidity of their mo- 
tions in different parts of their sinuous, and often in- 
voluted, courses recorded. Numerous cycles had 
been discovered which enabled the astronomers to 
regulate the calendar, predict eclipses, and foretell 
other astronomical conjunctions. Some of these 
cycles, like the cycle of Meton, — which is still used 
for calculating the time of Easter, and in which the 
Golden Number is the number of the current year, — 
are so extended that their discovery implies the 
maintenance of observations and the preservation of 
the records through long periods of time. In addi- 
tion to all this the great circles of the celestial sphere 
had been marked out, the equinoctial and solstitial 
points had been fixed, and Hipparchus himself had 
discovered the precession of the equinoxes. Lastly, 
the spherical form of the earth had been recognized, 
and some approach had been made to a knowledge 
of its dimensions. 

The circumstance that the vault of the sky forms a 
sort of natural map on which the paths of the planets 
and of the moon can be directly traced by the un- 
aided eye, and that of the sun readily inferred from 
what was called the ** heliacal " rising and setting of 
known stars, in connection with the religious impor- 
tance attached to the subject, was undoubtedly the 
reason that the ancients acquired an acquaintance 



THEIR PRACTICAL KNOWLEDGE. 47 

with astronomical facts so far beyond their general 
knowledge of natural phenomena; and it is not to 
the credit of our modern education that the learned 
men of those early times had a better acquaintance 
with the changing appearances of the spangled dome 
of heaven than any of our scholars at the present 
day, except those who especially devote themselves 
to astronomical studies. It is certainly a matter of 
great regret that our methods of education should 
not invite our children to observe what is going on 
around and above them. With the help of diagrams 
and orreries they learn from more or less popular 
text-books the outlines of the modern system of 
astronomy, and perhaps gain some conception of the 
immensity of space ; but they remain ignorant of the 
appearances which the skies unroll every clear night 
before their eyes. 

When looking from my summer home towards an 
uninterrupted eastern horizon I have often heard in- 
telligent people express surprise that the full-orbed 
moon which rose from the waves the previous night 
should rise behind the hills the next; and although 
this maybe an unusual experience, I question whether 
many of the graduates of our colleges have a clear 
conception of the singular involutes which the plan- 
ets would be seen to follow if each left a shining track 
in its wake; and certainly still fewer have any idea of 
the very tortuous course of the moon in her succes- 
sive lunations, until after a long period she retraces 
very nearly the same course again. But these are 
the very phenomena out of which our system of as- 
tronomy was constructed; and if we would under- 



48 COPERNICUS. 



stand what the great astronomers did we must first 
become acquainted with the appearances whose coils 
they unwound and whose complexity they unravelled. 
During the long night of the dark ages which suc- 
ceeded the fall of the Roman Empire, the records of 
ancient astronomy were preserved at Bagdad, at Cairo, 
and at Cordova, those centres of Moslem culture. 
With the revival of learning in the Christian world, 
soon after the capture of Cordova by Ferdinand the 
Third, of Castile, in 1236, astronomy became a favor- 
ite subject of study throughout Europe, and in this 
study the " Almagest " of Ptolemy was the great au- 
thority ; and two centuries and a half later, just at the 
dawn of the Reformation, when Ferdinand and Isa- 
bella were raising the united standards of Aragon and 
Castile on the last stronghold of the Moors in Spain, 
where Columbus was present seeking from their Cath- 
olic Majesties commission and supplies for his first 
memorable voyage, there was at the University of Cra- 
cow in Poland a young student, named Nicholas Co- 
pernicus, who was soon to become the greatest master 
of the astronomical knowledge of his age. After 
finishing his course at Cracow, Copernicus studied 
astronomy first at Bologna, then at Padua, and after- 
wards at Rome ; but having gained the highest honors 
at these great seats of mediaeval scholarship, and the 
reputation of being the most learned man of his time, 
at the age of thirty he retired to the little town of 
Frauenburg in eastern Prussia, where he spent the re- 
maining forty years of his life as a tender and devoted 
pastor of a rude and ignorant flock. To Frauenburg 
Copernicus had carried a grand conception, and in 



COPERNICUS. 49 



his simple lodgings, still shown in the neighboring 
hamlet of AUenstein, that conception was matured. 

The astronomy of which Copernicus was so great 
a master was the science constructed by Hipparchus 
and illustrated by Ptolemy, and which had remained 
essentially unaltered for more than a thousand years. 
The chief 'merit of existing treatises was the wealth of 
facts, and the records of conscientious observations 
which they contained ; and Copernicus was as famil- 
iar with the dubious ways of the celestial wanderers 
as is a shepherd with the by-paths of his straying 
lambs. His knowledge, moreover, was not mere eru- 
dition ; but the facts were ever present with him, and 
the paths of the heavenly bodies were engraved as 
clearly on the crystal sphere of his imagination as if 
on the firmament they were marked with a shining 
thread among the stars. 

But all this real knowledge came to Copernicus in 
the guise of a system which, although based on as- 
sumption, was consecrated by authority and tradition, 
and held by the learned world with the same rever- 
ence with which it still honors the models of clas- 
sical literature. As the earth was regarded as the 
centre of the universe, and the circle as the most 
perfect of figures, the astronomers assumed that the 
heavenly bodies must move around this globe in cir- 
cular orbits. But as the involutions of the planetary 
paths were obviously inconsistent with this simple 
assumption, Hipparchus sought to explain the an- 
omaly by what has ever since been known as the 
system of epicycles. The planets were assumed to 
move in circular paths around an immaterial point, 



50 COPERNICUS. 



which was itself moving in a circle around the earth ; 
just as if the planets were fastened to the rim of a 
vast wheel, revolving in a plane passing through the 
earth, while the wheel was rolling round the crystal 
sphere which formed the celestial vault. Perhaps the 
wheels of the chariot of the Sun in the Greek mythol- 
ogy suggested the idea ; and absurd as it seems to us, 
it was not inconsistent with the philosophy of motion 
taught by Aristotle, and universally held even at the 
time of Copernicus. In its more abstract form the 
conception had indeed an element of truth, and has 
been preserved by modern astronomy in the devices 
of mathem.atical analysis for computing a planet's ap- 
parent place. That such a device would give a gen- 
eral explanation of the stationary and retrograde 
phases in the planetary motions is obvious. But to 
the Ptolemaic school the conception was of far greater- 
value than this. By carefully collating and plotting 
observations, they were enabled to determine the 
periods of revolution both in the epicycle and in the 
cycle, and thus they calculated tables predicting the 
planets' positions; which, although vastly inferior 
both in accuracy and reach to similar tables in our 
nautical almanacs, were wonderful achievements for 
the time, and tended to give great confidence in the 
theory on which the calculations were based. 

To rude observation the motions of the sun and 
moon are far more regular than those of the planets ; 
and Hipparchus was able to explain the anomalies, 
so far as they were known to him, by a theory of 
eccentrics which placed the earth, not at the centre 
of the circles around which these great luminaries 



COPERNICUS. 5 1 



moved,"but at another point some distance from the 
centre, called the equant. As before, the conception 
was perfectly definite, and received a quantitative ex- 
pression. The position of the earth with regard to 
the centre of motion was determined, the points of 
apogee and perigee in the heavens were marked out, 
and from these data Hipparchus calculated tables of 
the sun and moon. In the time of Ptolemy, when 
the inequalities of the motions of all the heavenly 
bodies were better known, it became necessary to add 
epicycle to eccentric in order to reconcile the obser- 
vations ; and the result was a most complex system, 
which is graphically described by Milton : — 

"... how gird the sphere 
With centric and eccentric scribbled o'er — 
Cycle in epicycle, orb in orb ! " 

This was the system in which Copernicus was edu- 
cated, and by whose traditions and methods he must 
have been more or less bound. It would be very 
easy to misrepresent this system, and thus to under- 
value the work of Copernicus, by showing how ab- 
surd and childish were the theories he overthrew. 
In many of the materialistic aspects in which it was 
presented by classical writers, with its mechanism of 
crystalline spheres, it does seem as if the Ptolemaic 
system must have appeared to thinking men even 
then incredible and monstrous ; and one sympathizes 
with the King of Castile, who, when the system was 
explained to him, is said to have remarked that, '*if 
God had consulted him at the Creation, the universe 
would have been made on a better and simpler plan." 



52 . COPERNICUS. 



But when regarded abstractly, as the resolution of 
unequal motions of the heavenly bodies into two or 
more equable circular motions, it was not only a legi- 
timate scientific method, but is closely analogous to 
the empirical methods followed at the present day to 
connect a series of observations in any department 
of physical science when, as is usually the case, the 
dynamical causes are unknown ; and, as before inti- 
mated, is essentially the same method which is fol- 
lowed by the modern astronomer when he resolves 
unequal motions into a series of terms or expressions 
of partial motions involving the trigonometric values 
of circular arcs. 

This point, which has been so well made by 
Whewell, should be strongly emphasized. The dy- 
namical law which governs the motions of the heav- 
enly bodies was wholly unknown until discovered by 
Newton ; and as a system of calculation the theory 
of Hipparchus was not only good, but, as Whewell 
adds, ** no better has yet been discovered ; " and the 
maze of epicycles is simply the complexity which 
the calculations of apparent place in astronomy al- 
ways present. Moreover it appears very plainly 
from the writings of Ptolemy that his school regarded 
the whole machinery of epicycles and eccentrics as 
imaginary, and used them simply as devices for the 
graphical representation of apparent motions. As 
such they are true expressions, and the best that 
have been yet devised. Indeed more than one half 
of our modern physics rests on no better basis to- 
day. We have learned, however, to dissociate our 
partial generalizations from the material symbols in 



COPERNICUS. 53 



which they find expression, and are content to use 
these aids as guides so long as they lead us aright, 
and to wait until advancing knowledge shall give to 
them a wider and a fuller significance. The tendency 
among the ancients was the very reverse of this. They 
sought to materialize everything, as their mythology 
so plainly shows. But at the same time we have 
the best of evidence, as in the works of Ptolemy, that 
their more gifted minds rose superior to this spirit, 
and were able to discern the true ideal under the 
conventional dress of the symbols they habitually 
employed ; and it may be questioned whether the 
" crystalline spheres " by which in the imagery of 
their poets the complex motions of the heavens were 
maintained are one whit more absurd than the " lumi- 
niferous ether," without substance but with indefinite 
elasticity, with which modern science has filled the 
inter-planetary spaces. 

If we would appreciate what Copernicus achieved 
we must remember that he was educated in the sys- 
tem whose striking features we have been attempting 
to sketch, — a system which had all the authority of 
tradition, all the charm of antiquity, all the attrac- 
tions of learning, and beneath its conventional sym- 
bols all the sanctions of sound philosophy and all the 
spirit of true science. 

We are familiar with the outlines of the Coper- 
nican system, and I trust are now prepared to see 
clearly just what this great master contributed to the 
world's real knowledge, just how far his keen intellec- 
tual vision was able to penetrate the darkness of the 
then unknown. It can be stated in a few words ; for 



54 COPERNICUS. 



the offering which any man, however great, can bring 
to the altar of truth, though relatively it may be 
large, is always absolutely very small. 

Amidst the complexities of the apparent, Coperni- 
cus discovered the simpHcity of the real. He saw 
law under inequalities, regularity under variation, 
order under confusion ; and having gained a ghmpse 
of the true structure of the solar system, he showed, 
by a careful comparison of the theory with observa- 
tions, that the facts of nature harmonized with this 
conception. The large knowledge, the grand con- 
ception, the scrupulous confirmation, — these were 
the essential and inseparable stages of this grand dis- 
covery. 

Popular writers on astronomy often lay great stress 
on the statement that a heliocentric hypothesis was 
a favorite tenet among the disciples of Pythagoras, 
and therefore not original with Copernicus. But if 
they cite this well-known fact in disparagement of 
the work of the great father of modern astronomy, 
they must wholly misconceive the character of a 
scientific induction. - Those speculative philosophers 
of antiquity did not place the sun in the centre of 
the solar system on any basis of facts, but merely as 
an idle fancy by which they sought to pay honor to 
the sun-god. How utterly difi"erent with the system 
of Copernicus ! This was not only an inference from 
the largest knowledge of facts which the best scholar 
of his age could gain, but was also an inference veri- 
fied by observation, and by the most exact meas- 
urements which could then be made. Unverified 
hypotheses are accounted of no value in exact science, 



COPERNICUS. 55 



and in the opinion of competent judges no such an- 
ticipations in the least detract from the merit of a 
real discovery. 

It is not the least among the noble qualities of this 
hero of science that throughout all his work he dis- 
played such deep humility of spirit and such profound 
reverence for truth. His system must have been 
matured soon after he settled at Frauenburg, if not 
before. It was a vision of his youth over which he 
thought and worked for forty years before he told it 
to the world. He did not hasten like a young knight 
to slay the dragon which had guarded so long the 
opening of the pathway to the great treasure. He 
did not at once enter the lists against the defenders 
of old dogmas, because they were antiquated and 
seemed to him erroneous. Truth was sacred ; but 
so was just authority, so was noble learning, so were 
old institutions. And truth could wait ; and truth did 
wait, fresh and unimpaired, long, long years. In those 
lonely lodgings at Allenstein amidst the humblest 
pastoral and charitable duties, he questioned night 
after night that vision of his youth, multiplying ob- 
servations and repeating calculations, until the truth 
grew upon him with such conviction that he could 
no longer be silent ; and then he declared it, in spite 
of interest, in spite of opposition, in spite of contumely, 
in spite of persecution. 

In the long record of illustrious men who have 
devoted their lives to the advancement of knowledge 
for truth's sake alone, I know of no incident more 
impressive, more truly sublime, than that which is 
narrated of the death of Copernicus. The forty 
5 



56 COPERNICUS. 



years of patient labor in confirmation of the early 
vision had passed. The book had been written, and 
under great opposition had been printed at Nurem- 
berg. The last revisions had been made; but the 
author, worn out at seventy years with labor and 
anxiety, lay dying without any token of the travail 
of his soul. Indeed reports have come that bigotry 
has succeeded in stopping the publication for which 
his life has been spent, and all hope has fled, — when 
at the last moment a special messenger arrives, and 
places in the hands of Copernicus the long expected 
volume fresh from the press. The dying man is just 
able to return a sign of recognition, and whisper the 
final prayer, '' NUNC DIMITTIS SERVUM TUUM, DOM- 
INE ! " 

Were study always conducted in the spirit in which 
that book was written, the harmony of all real knowl- 
edge would become clearly manifest. In the dedi- 
cation of the work '' De Revolutionibus Orbium 
Coelestium" to Pope Paulus III., Copernicus ex- 
pressly states that he has kept his book by him 
for four times the nine years recommended by Hor- 
ace ; and remarks that ** the study of a philosopher 
is to seek out truth in all things so far as is permitted 
by God to human reason." 

The Copernican system was not at once generally 
accepted. Long cherished doctrines with their pre- 
scriptive rights are not so readily set aside ; nor is 
it well that they should be. But the system did very 
soon receive from astronomers that form of recog- 
nition which would most have pleased its author. 
In 1 55 1 Reinhold published tables, or " ephemerides," 



COPERNICUS. 57 



as they are usually called, based on the principles of 
Copernicus, whose verified predictions tended greatly 
to strengthen his theory ; and the demonstration was 
complete when in 1610 Galileo's new telescope re- 
vealed to sight, in the system of Jupiter's satellites, a 
model on a small scale of the solar system according 
to the views of Copernicus, and not long after showed 
that Venus had phases like the moon, thus making 
visibly manifest the planet's relation to the sun ; so 
that in less than a century after the death of its au- 
thor, in spite of prejudice and in spite of theological 
rancor, the heliocentric theory was almost everywhere 
received by learned men as an established doctrine 
of astronomical science. It is a striking illustration, 
however, of the conservatism of philosophical thought 
that Lord Bacon, who lived until 1628, long after the 
decisive discoveries of Galileo, never gave his assent 
to the Copernican doctrine, and even Descartes, who 
lived until 1650, gave to it at most only an implied 
recognition, rejecting the form while he adopted the 
substance. 

We can readily account for the position of Des- 
cartes, who had a theory of his own which seemed 
to him to include all that Copernicus had discovered ; 
but we cannot but be surprised that Bacon was so 
blind. It is one thing, however, to think and write 
learnedly about induction, and another thing to make 
discoveries. Bacon was a metaphysician, not a phys- 
icist, much less an astronomer. He had not the 
familiarity with nature by which alone an insight into 
her methods and processes can be gained. He could 
not therefore comprehend the vision of Copernicus, 



58 COPERNICUS. 



and it seemed to him a dream. To his introspective 
mind the order and finish of the Ptolemaic system 
had a great charm ; and he was bound hand and foot 
by traditions while protesting against them. Should 
we have been wiser? And may not his experience 
lead us not only to honor more highly the great man 
whose character I have sought to portray, but also 
to appreciate more fully, and value more highly, that 
wonderful power by which he accomplished such 
great results? 



TYCHO BRAKE. 



59 



LECTURE III. 

THE INDUCTION OF NEWTON. 

DURING the fifty years that followed the death 
of Copernicus, preparations were being made 
for another great advance in the theory of astron- 
omy. These preparations consisted chiefly in the 
extension of observations, the calculation of tables, 
the improvement of methods, — all resulting in the 
collection of fuller and more accurate data in regard 
to the motions of the heavenly bodies. A very skil- 
ful observer appeared, the accuracy of whose meas- 
urements exceeded anything that had yet been 
obtained. Copernicus had declared to a pupil, who 
was disturbed about single minutes, that " if he could 
be sure to ten minutes of space, he should be as 
much delighted as Pythagoras was when he dis- 
covered the property of the right-angled triangle ; " 
but it was claimed for Tycho Brahe that an error of 
eight minutes in his observations was impossible. 

In the last year of his life at Prague Tycho re- 
ceived into his observatory, as an assistant, a young 
man named Johann Kepler, who with these eight 
minutes, to use his own boastful words, was able to 
reconstruct the whole of astronomy. There could not 
be a greater contrast than that between Copernicus 



6o KEPLER. 



and Kepler, — the one, the ideal philosopher; the 
other, a veritable astronomical Don Quixote, turn- 
ing what he must have known to have been a dishon- 
est penny by astrology in his youth, and in his mature 
manhood discussing like a Lothario the qualifications 
of eleven different damsels to become his second 
wife. There never was a wilder imagination than 
that of Kepler, and he gave it full rein. The wisest 
of men have doubtless at times idle fancies ; but then 
they have the wisdom to keep their folly to them- 
selves, or at least to their homes. Kepler, on the 
other hand, seems to have had no sense of decorum. 
He not only entertains and cherishes the most ab- 
surd speculations, but he publishes them all to the 
world; so that his voluminous works are a most 
singular medley of sound thoughts and unmitigated 
nonsense. But beneath all this there is the true sci- 
entific spirit. He submits his ridiculous conceptions 
to the test of experience, and rejects them at once 
if they do not stand the trial. He displays without 
reserve all the inner processes of his thoughts, ex- 
aggerating his follies, and parading his conceits like an 
actor ; and this makes his works a curious study of 
the inductive method of reasoning; for among all 
these wild guesses he discovered three great truths, 
which have ever since been known as Kepler's Laws, 
and which will render his name honored so long as 
astronomy is studied. 

Copernicus had divined the great central feature 
of the solar system, but he was trammelled to the 
last by the Aristotelian dogmas in regard to the na- 
ture of motion, and assumed throughout that the 



KEPLER. 6l 



heavenly bodies must maintain an equable circular 
motion m their orbits ; and in order to explain the 
obvious anomalies which remained, even on his helio- 
centric theory, he was obliged to retain the system 
of eccentrics and epicycles of the Ptolemaic school, 
although very greatly reduced in proportions. This 
was a manifest blemish on the Copernican system ; 
but these devices were evidently regarded by Coper- 
nicus as temporary modes of representing the irreg- 
ularities, for the purposes of computation. And it 
must be remembered that in physical science appar- 
ent irregularities are inseparable from observation 
and experiment ; and that the most conspicuous feat- 
ure of modern astronomy is the discussion of just 
such seeming discrepancies, only of course of a much 
lower order of magnitude. In reducing the magni- 
tude of the anomahes Copernicus recognized that 
he was approaching a true theory ; and in the study 
of nature this is all any man is permitted to do. The 
inmost shrine cannot be entered ; and Copernicus 
did not feel the necessity of reconciling his empirical 
methods with modern dynamics. 

Kepler had no better knowledge than Copernicus of 
the laws of motion, — although he was a younger man 
by seven years than Galileo, and the experiments 
of the Pisan professor on falling bodies, and his sar- 
castic attacks on the notions of the Aristotelians, had 
been published long before the famous laws of plan- 
etary motion were discovered. Kepler not only held 
to the dynamical conceptions of Aristotle, but put 
them into the most grotesque guise, likening the 
planets to huge animals rushing through the skies. 



62 KEPLER. 



He was not, however, hampered by deference to dog- 
mas of any kind. He had no more respect for a 
circle than for any other curve ; and since an oval, 
like a circle, returns upon itself, and would thus obvi- 
ously satisfy one fundamental condition of a planet's 
orbit, he inquired, with the aid of careful plottings 
and computations, how far observations of positions 
in the case of the planet Mars could be satisfied on 
the assumption of an oval orbit. 

In the first place he found that by considering the 
plane of the planet's orbit with reference to the sun 
alone, a position could be given to this plane from 
which the planet had none of the librations which 
both Ptolemy and Copernicus had attributed to it. 
Copernicus, influenced evidently by his Ptolemaic 
education, had assumed that the orbits of the planets 
must have some connection with the plane in which 
the earth moved ; and this simple step of Kepler's 
at once freed the heliocentric theory from the ma- 
chinery of epicycles with which Copernicus had left 
it encumbered. 

But the eccentrics remained, for they were facts 
of nature ; and it was then apparent that the planet 
did not have an equable motion in its orbit, as had 
been until then assumed ; so that with the epicycles 
the old dogma of equable circular motions was ban- 
ished forever from astronomy. Thus freed from a 
blinding prejudice, Kepler was soon able to take a 
great step forward. In studying the conditions which 
on the new theory regulated the changing velocity 
of the planet's motion in different parts of its orbit, 
he discovered what has since been known as Kepler's 



KEPLER'S LAWS. 63 



" Second Law," that the areas described, or swept, 
by the line drawn from the planet to the sun are 
always equal in equal times, or are proportional 
to the durations of the motion. The ** First Law," 
that the orbits of the planets are true ellipses, 
of small eccentricity, with the sun at one of the foci, 
was not reached until some time after the " Second 
Law," and the step between the two was a very long 
one for Kepler. He tried all sorts of hypotheses 
of circular and oval orbits before he hit on what 
would seem to us the most obvious conception of 
all ; and the detailed history of his struggles with 
this problem occupies thirty-nine chapters of his 
work " De Stella Martis. " The *' Third Law," that 
the squares of the periodic times of the planets are 
proportional to the cubes of the solar distances, 
had in Kepler's mind no logical connection with the 
first two, but was the one valuable result of the ex- 
travagant and often preposterous speculations which 
he narrates at great length in his book on '* The 
Harmonies of the Universe." 

There is a great deal in Kepler's character which 
might naturally impair that respect for the scientific 
investigator which the graces of Copernicus have 
done so much to establish. It seems inscrutable that 
such a *' krank," as Kepler appears in a large part of 
what he wrote, should have accomplished such great 
results; and it would be natural to judge the work 
by the man. But this was not the first case in which 
*' God hath chosen the foolish things of the world to 
confound the wise; " and it is possible that just such 
a man was required to break up the superstitions 



64 KEPLER'S CHARACTER. 

which the dogmas of Aristotle had become. And 
however weak in some of the relations of life, Kepler 
united all the conditions of successful induction. He 
had a very large knowledge of astronomical facts, and 
was familiar with all their Hmitations. He had an 
exuberant imagination, and great fertility of invention. 
He was loyal to nature, and never harbored his errors 
when once refuted. As Whewell very justly says, 
''Kepler certainly was remarkable for the labor which 
he gave to such self-refutations, and for the candor 
and copiousness with which he narrated them; his 
works are in this way extremely curious and amus- 
ing, and are a very instructive exhibition of the 
mental process of discovery." 

To illustrate the characteristic features of the in- 
ductive method here referred to is the chief object of 
these lectures ; and I trust that the story of Kepler 
has made prominent three essential conditions of 
success : first, a large knowledge of facts, based on 
an intimate acquaintance with the phenomena of na- 
ture ; secondly, a fertile imagination, ready to sug- 
gest the possible relations of these facts ; thirdly, a 
conscientious scientific spirit, which submits every 
hypothesis to the test of observation or experiment. 

The laws of Kepler were purely formal ; that is, 
they were expressions of facts or relations for which 
no explanation was given, or could be given at that 
time. It was a fact that the planets moved in ellip- 
tical orbits ; it was a fact that the radius vector swept 
over equal areas in equal times ; it was a fact that the 
squares of the periodic times were proportional to 
the cubes of the sun's mean distance; and the cir- 



FORMAL AND DYNAMICAL LAWS. 6$ 

cumstance that these facts were learned by inference, 
and not by direct observation, does not alter their re- 
lation to the scheme of knowledge. They are in no 
respect efficient causes. They are simply facts and 
nothing more, and to Kepler they were wholly dis- 
connected facts ; and this distinction between a for- 
mal or phenomenal law, which merely expresses a 
general fact of nature, and a dynamical law, which 
gives the mode of action of an efficient cause, corres- 
ponds to a most important step in the progress of 
science. We can distinguish three stages in this pro- 
gress: first, the phenomenal stage, in which only 
isolated facts are observed and recorded ; secondly, 
the formal stage, in which facts of general relation- 
ship are discovered ; thirdly, the dynamical stage, in 
which the relations are traced to some efficient cause. 
Astronomy was raised to its second stage by Hippar- 
chus, to its third stage by Newton. Until the end 
of the seventeenth century it was still in the formal 
stage, and the discoveries of Kepler did not alter its 
position, although they prepared the way for the 
great advance which was soon to follow. According 
to Kepler's loftiest conceptions the planets moved in 
the manner which he had discovered simply because 
it was their nature so to move. But a far more gifted 
seer was soon to come, who should show that the laws 
of Kepler were the necessary and very partial re- 
sults of the action of a force which controlled the 
universe. 

If after his work was done Kepler had been told 
that in less than a century the laws he had discovered 
would be shown to be merely phases of the action of 



66 KEPLER'S IDEA OF FORCE. 

universal gravitation, there can be little doubt that he 
would have regarded the prophecy as grandiloquent 
nonsense. Kepler associated no clear conception 
with the word '' force," and did not recognize a force- 
of gravitation. By Kepler, and by all scholars before 
him, as well as by many after him, the word ** force " 
was used to denote any manifestation of energy, which 
might vary widely not only in its nature but also in 
its mode of action. There were forces innumerable, 
each with its own special virtue and mode of action. 
It was obvious then as now that muscular force would 
produce motion, and that a moving body would exert 
force ; but there were no clear conceptions of the re- 
lation of motion to force. A stone fell to the ground, 
not because it was pulled by a force which we now 
call gravity, but because it was the tendency of heavy 
bodies to move downward, through a virtue residing 
in the body itself, not in the earth. It must have been 
known to Kepler that while he was at work on the 
theory of Mars an Italian named Galileo, with whom 
subsequently he maintained a friendly correspond- 
ence, had been making some curious experiments on 
swinging pendulums and falling bodies, which were 
subversive of all the old mechanical notions ; but he 
did not dream that they had any bearing on his 
studies. Yet Galileo was doing for mechanics almost 
precisely what Kepler was doing for astronomy, and 
the labors of both men were the necessary prelude to 
the induction of Newton. In order that we may the 
better understand the bearing of this new and con- 
verging line of investigation it may be well for me to 
review very briefly the fundamental conceptions of 



FORCE AND MOTION. 6/ 

the modern theory as to the relations of motion and 
force. 

We know nothing more about the origin of force 
than our fathers, but we have a very clear idea about 
the uniformity of its manifestation. Force, however 
produced, always manifests itself either as a pull or a 
push, and no matter what may be the circumstances, 
this pull or push varies only in strength. The farce 
may be produced by muscular action ; it may be due 
to electrical excitation ; it may be an effect of mag- 
netism; it may be caused by heat; it may be grav- 
ity ; but in all these cases the ultimate effect is a pull 
or a push. We do not, of course, by this analysis, 
remove in the least degree the mystery which still 
surrounds the origin of force; we know nothing 
more about the nature of gravity than we knew be- 
fore : but we do know that gravity acts as a pull of 
definite strength ; and we have made a great advance 
towards clear thinking when we have been able to 
banish from our minds all the indefinite and mys- 
terious accessories with which the term has been as- 
sociated, and whenever the word " force" is used, to 
think only of a pull or a push between two definite 
bodies. So also with motion. It would be easy to 
bewilder the imaginatipn by attempting to combine 
the various motions of which every object on the sur- 
face of the earth must simultaneously partake; or 
confuse the mind by discussing whether independent 
motion in space is oonceivable. But in physics we 
deal only with relative motions. We do not recog- 
nize absolute rest or motion. An object is at rest or 
in motion solely with reference to some other object. 



68 FORCE AND MOTION. 

A body, therefore, may be at the same time at rest 
in relation to one object and in motion in regard to 
another. If two bodies are moving with relation to 
each other it is wholly arbitrary which is regarded as 
at rest and which in motion. It is not necessary to 
dwell on illustrations of these points, which the mov- 
ing trains on our railroads so frequently bring to 
mind. Rest and motion in mechanics are, therefore, 
simply relative states, and should only be considered 
from this point of view. Never think of motion as 
an attribute of a body, but only as change of place 
with reference to some other body. If the old Greeks 
could have realized this simple conception the prog- 
ress of astronomy would have been hastened by at 
least a thousand years. 

It will now be seen to be an obvious phase of the 
fundamental conception, that the same body may par- 
take of several motions at once, and that each of these 
motions will be entirely independent of the others, 
and uninfluenced by them ; so that the resulting path 
and final goal will be simply the combined effect of 
all. This conclusion, if not at once obvious, will ap- 
pear if it is remembered that according to the fun- 
damental conception of motion, a body assumed to 
be at rest in relation to several other bodies assumed 
to be in motion is in the same condition towards 
each one as if these assumed states were reversed ; 
and hence, that its relations to the several bodies 
must be as independent in one state as in the other. 
Thus arise all the familiar principles of the composition 
and resolution of motions, which, however complex in 
some of their applications, are very simple in theory. 



DIRECTION. 69 



As with motion, so also in regard to direction, we 
have only relative knowledge. It is useless to inquire 
whether we could form any idea of direction indepen- 
dently of the objects around us ; and it was merely 
their limited acquaintance with the dimensions of the 
universe which led the Greeks to speculate about 
absolute directions. Upward and downward have 
reference solely to the earth; and directions can be 
known only in relation to the positions or features of 
material bodies. Practically, we refer both direction 
and motion to the earth, with its fixed axis and con- 
stant time of rotation, and with well marked features 
on its surface ; and we come to associate our ideas of 
motion and direction solely with this standard. But 
we should bear in mind that this standard, though 
natural, is arbitrary, — that other standards might be 
used, and are used in astronomy. When in analytical 
geometry or crystallography we refer directions and 
positions to a set of arbitrary lines called axes, we 
merely do for our problems what nature has done 
for our every-day life, by placing us on a globe with 
definite outlines which set bounds to our habitation, 
and fixed limits on which our thoughts may rest. 
To the young student of mathematics all this sys- 
tem of co-ordinates, with the arbitrary transforma- 
tions, seems very artificial; but they are essential 
conditions of clear thought ; and it was the want of 
the very conception which they embody which made 
the method of Euclid so limited in its applications. 

Few works that have come down to us so strik- 
ingly illustrate the fertility, acuteness, and versatility 
of the Greek mind as the " Geometry of Euclid ; " and 



70 DEFECT OF THE GREEK GEOMETRY. 

it remains to our time one of the chief tools in educa- 
tion. As a training in intellectual gymnastics it is an 
admirable study, but as a means of investigating na- 
ture it is practically useless ; and the defect of the 
Greek geometry, like the defect of the Greek me- 
chanics, arose from seeking the fundamental con- 
ceptions, not in the observation of nature, but in the 
accidents of thought, — although, from the nature of 
the subject, the first defect was, of the two, far the 
less serious in its consequences. This defect appears 
conspicuously in Euclid's treatment of the straight 
line, which is defined as the shortest distance be- 
tween two points ; leaving out of account the funda- 
mental characteristic, that of definite direction. The 
Greeks were, with reason, very proud of their ge- 
ometry ; but the science could not measure the earth, 
as its name denotes, much less the heavens, until it 
was re-established by Descartes on the basis of accu- 
rate conceptions of direction. Even at the present 
day, since most of us have derived our knowledge 
of geometry either directly or indirectly from Euclid, 
it is not unimportant to insist that direction, like mo- 
tion, is a fundamental condition or state, inseparable 
from material existence, whose relations we must ac- 
cept as facts of observation, and not merely as modes 
of consciousness. 

With the fundamental conceptions clearly estab- 
lished, see how very simple all the relations of force 
to motion at once become; and how intelligible, in 
the light of our familiar experience. If a body is at 
rest with reference to another it can be set in motion 
only by the application of force, — that is, by what 



LAWS OF FALLING BODIES. 7 1 

is the equivalent of a pull or a push between the two ; 
if it is in motion it can only be brought to rest in the 
same way ; and to start a body when at rest, or to 
stop it when moving, are, mechanically, equivalent 
operations. 

When a constant force acts on a body in the direc- 
tion of its motion, the velocity of the motion must be 
constantly accelerated, because the effect of the pull 
at any instant must be added to the previous condi- 
tion. Remembering that the pull or push at each 
instant simply adds its effect to the previous state, 
it will be seen that the laws of accelerated or re- 
tarded motions — including the laws of falling bodies 
— follow at once from the fundamental principles ; 
and that acceleration or retardation are indications of 
the action of some force; and that the amount of 
acceleration or retardation is the measure of that 
force. If a body is acted on by two or more forces 
at once, each produces its effect independently of the 
others, and the final result is found by simply com- 
bining the several effects. 

Evidently, very complex problems may arise under 
the conditions last named. One of the simplest is 
when a bomb-shell is thrown from a mortar. The 
exploding gunpowder gives to the ball a tremendous 
push in a given direction, and were it not for the 
pull of the earth and the resistance of the air, — which 
last we here leave out of the account, — the ball, with 
reference to the gun, would move on forever and 
with a uniform velocity; but the moment it starts 
from the gun it begins to fall to the earth, and falls 
the same number of feet in a given time that a stone, 
. 6 



72 PROBLEM OF CENTRAL FORCES. 

or any other object, would fall if dropped from an 
elevation. The actual path is a combination of the 
two motions, and would be a parabola were it not 
for the resistance just referred to. Another and some- 
what similar problem assumes great importance from 
its astronomical relations. A body is moving with 
reference to another, and much more massive, object, 
which for distinction we will call the central body, — 
not directly to or from it, but on a line which leaves 
the central body on one side at a greater or less 
distance. On this moving mass the central body 
exerts a constant pull. What will be the effect? 
This will depend on the strength of the pull ; but, 
in general, the path assumed by the moving body 
will be that of one of the conic sections, drawn 
round the central body as the nearer focus, and in a 
plane containing both this centre of force and the 
original path. If the force were comparatively feeble 
the body would describe the arc of an hyperbola, 
and fly off on a new course in the direction of the 
asymptote to this curve; but if the force were be- 
yond certain limits the path would be a circle or an 
ellipse returning on itself; and we should then have 
the counterpart of the motions of the planets. 

In this connection it is to no immediate purpose to 
inquire what was the cause of the primitive motion, 
unless as a matter of curious speculation about world- 
building; for the motion was a primitive state, just as 
much as the chemical elements or any other funda- 
mental conditions. The solution of the problem of 
central forces, as it has been called, is independent of 
such considerations, and is complete without them. 



THE THREE LAWS OF MOTION. 73 

With our present conceptions of force and motion it 
seems perfectly simple, and as given in our college 
text-books it can be followed by any scholar with a 
moderate knowledge of mathematics; but only two 
hundred years ago it taxed the best minds of an age 
remarkable for the powerful intellects it produced. 

From the primary conceptions of direction, motion, 
and force, it would be very easy to develop all the 
fundamental principles of mechanics, — to show that 
when a pull or a push acts between two bodies both 
must partake equally in the effect, or in other words 
that action and reaction rmust be equal and opposite, 
— to make evident that the mass of the bodies, as 
measured by their weight, is a most important factor 
in the result, and that the velocity imparted by a force 
of constant strength, other Ithings being equal, must 
be proportional to the amount of material on which 
the force acts, — to point out the distinction between 
tension, or pressure, and work, or between momen- 
tum and vis viva, a distinction which, although now 
so familiar, was during the eighteenth century the 
subject of a long and warm controversy among the 
most eminent mathematicians of Europe. But these 
points have only an indirect bearing on my present 
argument ; and I will close this summary of essential 
preliminaries with the statement of the three laws of 
motion as given by Newton in his *' Principia." First 
Law : Every body continues in a state of rest, or of 
uniform motion in a straight line, unless acted on 
by some external force. Second Law: Change of 
motion is proportional to the force impressed, and is 
in the line in which the force acts. Third Law: 



74 GALILEO. 



To every action there is always opposed an equal 
reaction. 

Although at the present day the relations of force 
to motion might be summarized to advantage in more 
general terms, yet these formulas show a perfectly 
clear conception, on the part of Newton, of the true 
relations, and indicate a wonderful advance in clear- 
ness of thought on this subject between the publica- 
tion of Kepler's work '' De Stella Martis " in 1608, 
and that of the " Principia" in 1686. This is not the 
place to follow in detail the history of this progress ; 
but we will touch on one or two points, of which the 
summary we have just given will enable you to see 
the bearings. 

Galileo — who was born in 1564, and became a 
teacher at the University of Pisa in 1589 — laid the 
foundations of modern mechanics; and chiefly by 
the remarkable series of experiments which he made 
at Pisa during the three years (1589-91). In gen- 
eral terms it may be stated that Galileo discovered, 
and verified by experiment as formal laws, most of 
the fundamental principles of dynamics. He taught 
that all matter has weight, and that gravity and 
levity are only relative terms. He pointed out the 
relations of the centre of gravity, and insisted 
that weight was a constant force, pulling all bodies 
towards the centre of the earth. He maintained that 
motion was the result of force, and clearly enunciated 
the laws of falling bodies, — illustrating the theory 
by experiments from the ** Leaning Tower of Pisa " 
which have become memorable in the history of sci- 
ence. He clearly distinguished between uniform and 



GALILEO'S DISCOVERIES. 75 

accelerated motion. He showed that motion caused 
by a single force is always in a straight line, — that is, 
in a definite direction ; but that under the influence 
of several forces a body may move in as many direc- 
tions at once, simultaneously and independently. He 
established the principle of the composition of forces, 
and gave the true theory of projectiles. He distinctly 
recognized, at least by implication, the principles of 
action and reaction, and even of virtual velocities. 
His works are full of ingenious demonstrations of 
mechanical theorems, both theoretical and experi- 
mental; and he was versatile as an experimenter 
as he was sound as a reasoner. But still, his results 
were for the most part formal, and not co-ordinated 
under general principles. Unquestionably, the prin- 
ciples of Newton's three laws of motion may be re- 
garded as implied in the whole tenor of Galileo's 
experiments and computations, but they are no- 
where definitely formulated in his writings, — although 
in the review of the principles of mechanics which 
he published near the close of his life he shows much 
more distinct conceptions of the nature and relations 
of force and motion than he did in his earlier work. 
This book, entitled " Dialoghi delle Nuove Scienze." 
and printed by the Elzevirs at Ley den in 1638, 
gained universal admiration, and drew wide attention 
to the subject. Like a well-known book, " Heat as 
a Mode of Motion," which has done a similar work 
in our own day, this last and best of the publications 
of the great Florentine familiarized men's minds 
with the interdependence of force and motion, which 
up to this time had been only a disputed doctrine 



76 GALILEO A POPULAR LECTURER. 

known to a few scholars. The works of GaHleo were 
among the most important means of education for 
the future Newton, and through them this noble 
father of mechanical science, as well as great dis- 
coverer in astronomy, was in fact one of the chief 
teachers of his far greater successor. 

In estimating the ability of Galileo and the merit 
of his labors, we must remember that, like Coper- 
nicus, he had to contend with the prejudices among 
all scholars in favor of the dogmas of Aristotle; 
which at the time were not only a belief but a reU- 
gion. Still, we cannot but regret that so much of the 
energy of this great originator was wasted in fruitless 
disputations with the upholders of the old doctrines, 
whom he followed with such pertinacity and bitterness 
that they became his violent enemies. In this, how- 
ever, he was but taking the course to which his disposi- 
tions and abilities inclined him ; for GaHleo had a 
most remarkable power both as an expositor and as a 
writer. He was what we should call a most success- 
ful popular lecturer ; and when, driven by the old 
schoolmen from Pisa, he accepted a professorship at 
Padua, a hall holding two thousand persons was pro- 
vided to receive the vast audiences which thronged 
to his lectures. 

It was his controversial spirit, rendered especially 
irritating by the great influence of his powerful utter- 
ance, which led to the collision of Galileo with the 
Papal authorities. At heart he was a good Catholic 
and a faithful son of the Church. He had many 
friends among the most influential of the clergy; 
and there can be no question that he would have 



GALILEO'S CONFLICT WITH THE CHURCH. ^'J 

been left to teach as he pleased, and even been 
honored^ for his innovations, if only he had avoided 
theological issues, instead of rushing into them. 
There was no need of forcing that greatly irritated 
lion caged at the Vatican to show its claws. Neither 
truth nor honor required it ; and though we may not 
think that a scholar can honorably hold an equivocal 
position in regard to facts of demonstration, yet the dis- 
tinction between ''ex hypothesi" and "exanimo" was 
one which Galileo avowedly accepted. And when he 
violated his pledges, and again revived the old issues, 
we cannot wonder that his conduct provoked censure ; 
and it may be questioned whether he was treated any 
more harshly than is many a man at the present day, 
for a much less departure from prescribed creeds. 

In the next generation after Galileo the theory of 
mechanics became much more clearly developed, and 
chiefly by his pupils or by those whom he directly 
influenced. Of this generation, although only surviv- 
ing Galileo eight years, was Descartes, one of the most 
powerful minds which the world has ever produced. 
Descartes, however, was a metaphysician rather than 
a physicist ; a better reasoner than observer ; a better 
mathematician than experimentalist. He never fully 
entered into the spirit of the inductive method, or 
made any far-reaching induction, — although he spent 
much time in experimental work, especially in phys- 
iology, and made some notable discoveries in phys- 
ics, particularly the cause of the rainbow. His theory 
of vortices, received with great applause at the time 
as a mode of explaining the motions of the heavenly 
bodies, and in its essential features revived of late in 



y8 THE INFLUENCE OF DESCARTES. 

connection with molecular physics, plainly shows that 
Descartes had not a clear appreciation of the funda- 
mental conceptions of mechanics. Nevertheless his 
enunciation — for little less can it be called — of the 
principle of the conservation of energy is an anticipa- 
tion of one of the very latest results of science, than 
which none more remarkable can be found in the whole 
history of speculative thought; and this prevision will 
appear still more wonderful when it is remembered 
that it involved the assumption of molecular motion, 
with the plain suggestion that heat may be a mani- 
festation of the internal motions of material bodies. 
Nevertheless, apart from his metaphysical writings, the 
great contribution that Descartes made to the world's 
progress was his geometry, to which we have before 
referred, and whose leading principle we have pointed 
out. Descartes not only gave a new life to this oldest 
of the sciences, but he endowed it with a power of 
interpretation which has done more than all other 
agencies combined to extend our knowledge of the 
heavenly bodies. 

Into a world thus prepared for a great revelation of 
knowledge was born, Christmas day, 1642, at the 
close of the very year in which Galileo died, the child 
who was to render illustrious his father's homely 
name of Isaac Newton. 

It is always highly interesting to study the career 
of a man who has fulfilled an important mission, — to 
attempt to discover inherited tendencies ; to trace the 
influences by which his mind was moulded ; to notice 
early indications of peculiar power, even if remark- 
able only because they seem prophetic ; to mark the 



EARLY LIFE OF NEWTON. 79 

guidings of opportunities, if not the leadings of Provi- 
dence ; to discriminate between native genius and ac- 
quired talent; to see force of intellect and of will 
rising superior to circumstances; or, what is often 
most singular, to find in the limitations of mental en- 
dowments a more potent influence than natural abili- 
ties in leading the specialist apart from the beaten 
track; to realize what were the conditions under 
which the great leader worked, and what were the 
materials at his command; and finally, to learn how 
small, after all, were the single steps by which he 
attained success. 

Unfortunately, we have only the most meagre out- 
lines of the early life of Newton. He does not seem to 
have been a precocious child ; and the tales of early 
mechanical skill are only such as are told of many a 
boy who has become only an ordinary man. Even at 
college — to which he appears to have been sent on 
an after-thought, like the weakly son of a New Eng- 
land farmer — there is no evidence that he gained 
great distinction; so that when, in 1667, at the age 
of twenty-five, two years after he received the Bach- 
elor's degree, he was appointed Fellow of Trinity 
College, Cambridge (his own college), we are sur- 
prised to find him in possession of a power of 
mathematical analysis far in advance of the best 
mathematicians of his day. He himself tells us that 
while an undergraduate he studied the Geometry of 
Descartes, which he had some difificulty in mastering; 
and already by his method of fluxions he had vastly 
extended the grasp of the new Cartesian instrument 
of research. 



8o HIS SYSTEM OF FLUXIONS. 

As is well known, ** Fluxions " was the name given 
by Newton to the Infinitesimal, or, as it is now more 
frequently called, the Differential and Integral Cal- 
culus ; and the advance made by the introduction of 
this new method into geometry was incomparably 
greater than any step which had hitherto been taken. 
It was, moreover, peculiarly an intellectual achieve- 
ment; and, although some advance had previously 
been made in the mathematical treatment of the in- 
finitesimal quantities of geometry, especially by Fer- 
mat and also by Barrow, Newton's predecessor in the 
Lucasian chair of mathematics at Cambridge, yet the 
improvement made by Newton was very great. That 
this improvement should have been made by an 
undergraduate was wonderful; and we find it diffi- 
cult to explain why it did not at once win admira- 
tion, and was not widely proclaimed and highly 
honored, except on the assumption that though 
far in advance of his instructors, Newton's abilities 
and attainments were Hmited to special lines, which 
did not at the time find favor among the university 
authorities. 

The method of fluxions, although from this early 
period constantly used by Newton in his own work, 
and doubtless taught by him as Professor of Mathe- 
matics, — an office which he filled at Cambridge from 
1669 to 1 701, — was not fully described in print until 
1691, and then not by himself; although the prin- 
ciple of the method was given in a geometrical form 
in the '^ Principia " four years earlier. It thus came to 
pass that in publication Newton was anticipated by 
Leibnitz, who, in the "Acta Eruditorum," Leipsic, 



THE CALCULUS OF LEIBNITZ. 8 1 

1684, described essentially the same method, though 
under a different name and with a different notation. 
In England Leibnitz was accused of borrowing his 
first conceptions from hints in letters of Newton, and 
no little bitterness on both sides was the result. But 
in the discussion which arose, while Newton's priority 
was established beyond a question, the originality of 
Leibnitz was also made equally clear ; and it is the 
notation and forms of Leibnitz, and not those of 
Newton, which have been retained in science. 

We do not know how early Newton applied his 
new calculus to the solution of the so-called problem 
of central forces. Since the principles of the compo- 
sition of forces had been established by Galileo it 
had become evident that the path of a planet might 
be, as we have already pointed out, the resultant of 
a primary motion of translation, modified by some 
power constantly pulling the body towards the centre 
of motion ; and the question was, what would be the 
form of the orbit under such conditions. Attention 
had been drawn to this problem in many quarters, 
but the resources even of the geometry of Descartes 
were not adequate to a complete solution. One con- 
clusion, however, quite plainly followed from the 
third law of Kepler, — although the complete demon- 
stration even of this point was first given by Newton, 
— and this conclusion was that if such a central force 
as had been assumed existed, it must diminish as the 
square of the distance from the sun; otherwise the 
squares of the periodic times of the different planets 
would not be proportional to the cubes of the dis- 
tances, as Kepler had found them to be. 



82 PROBLEM OF CENTRAL FORCES. 

As early as January, 1684, the problem of central 
forces was discussed by three eminent English mathe- 
maticians, Sir Christopher Wren, Halley, and Hooke ; 
but the discussion leading to no definite result, 
Halley, in August of the same year, went to Cam- 
bridge, to consult Newton on the subject; and without 
mentioning that a discussion had been held, " went 
straight to the point, and asked what would be the 
curve described by a planet round the sun, on the 
assumption that the sun's force diminished as the 
square of the distance." Newton replied promptly, 
** An ellipse ; " and on being questioned by Halley as 
to the reason for his answer, he replied, "Why, I have 
calculated it." That the calculation had been made 
some time previously is evident from the further cir- 
cumstance, we learn through Halley, that Newton could 
not at once put his hand upon his former work ; but he 
soon afterwards reproduced it, and in November sent 
Halley a copy of the result. Soon after, Halley again 
visits Cambridge to confer with Newton about the 
same problem, and these conferences led to the prep- 
aration of the " Principia," which was published under 
the auspices of the Royal Society, at Halley's own 
charge, two years later. The demonstration of the 
law of gravitation first appeared in the ** Principia ; " 
and it is a most noteworthy fact — which marks a mqst 
striking difference between the scientific activity 6f 
those days and the investigations of our time — that 
so important a result, which in all its essential features 
must have been reached at least ten years before, 
should have been kept so long by the author to him- 
self, and even by him so far forgotten that he could 



PROBLEM OF CENTRAL FORCES. 83 

not at once reproduce one of the chief steps in his 
reasoning. 

The problem of central forces as solved by New- 
ton involved, as we have seen, two distinct questions. 
In the first place, it was necessary to determine the 
rate according to which the central force varied with 
the distance ; and Newton had shown that it followed 
from the third law of Kepler that the force must 
diminish with the square of the distance ; but in this 
he had been to some extent anticipated. In the 
second place, assuming a force thus varying, it was 
required to find what would be the character of the 
orbit of a body revolving round the centre of force 
under its control. Newton was the first to answer 
this last question correctly, and he had shown, not 
only that the orbit would be an ellipse as the first 
law of Kepler required, but also that, as the second 
law required, the radius vector must describe equal 
areas in equal times. 

These results, however, had been deductions drawn 
from established principles of mechanics by the aid 
of the new calculus. No one thus far had suspected 
the nature of this central force ; and by most scholars 
of the period it would have been thought degrading 
to astronomy to associate the mechanism of the 
heavens with the mechanics of the earth. The two 
subjects were never thought of in the same connec- 
tions. There were, it is true, the deductions just re- 
ferred to, by which it appeared that the planets 
might be sustained in their motions round the sun by 
the action of a constant central force controlling their 
primary motions. There were also the undoubted 



84 LAW OF GRAVITATION. 

facts of mechanics, that weight was the effect of a 
direct pull or force exerted by the earth on all bodies, 
and that the strength of this pull was directly propor- 
tional to the amount of material on which it acted. 
As yet, however, these two classes of facts, so closely 
associated in our own minds, belonged to wholly dis- 
tinct categories of thought, and were no more asso- 
ciated than we connect the fluctuations of the market 
with the motions of the moon. Indeed that there 
was any intimate relation between force and motion 
was then a very modern conception. 

The idea, that, after all, this sublime, inscrutable, 
central force of astronomy was simple commonplace 
gravity seems suddenly to have flashed into the mind 
of Newton. We all know the anecdote of the faUing 
apple. The authority for the story is Voltaire, who 
narrates it in a somewhat popular account of New- 
ton's work, which he wrote for French readers soon 
after his return from England in 1729. He gives as 
his authority Catharine Barton, a favorite niece of 
Newton. She married Conduit, a Fellow of the 
Royal Society and one of her uncle's intimate friends, 
with whom also Voltaire was intimate during his well 
known residence in London from 1726 to 1729; and 
it was during this time, in 1727, that Newton died. 
The story has been discredited by Sir David Brew- 
ster in his ''Life of Newton ;" but, as must be admitted, 
it is as authentic as such a personal reminiscence 
could well be ; and it is certain that tradition marked 
the tree near his mother's house at Woolthorpe in 
Lincolnshire as that from which the apple fell, till 
1820, when owing to decay it was cut down, and the 



THE INDUCTION OF NEWTON. 85 

wood carefully preserved. Tradition also fixes the 
date as 1666, soon after Newton's graduation from 
Trinity, when he was passing several months at his 
old home on account of the fear of the plague at 
Cambridge. 

Why may not the force which pulls the apple pull 
the moon? We are left in no doubt whatever in re- 
gard to the general tenor of Newton's thoughts, 
either in the garden at Woolthorpe or elsewhere ; for 
we are told the story by Pemberton in the preface to 
his ** View of Newton's Philosophy," and he had it 
from Newton himself. If the power of gravity, New- 
ton thought, is not sensibly diminished at the greatest 
heights to which we can rise from the earth's surface, 
neither at the tops of the loftiest buildings nor even 
on the summits of the highest mountains, why may it 
not extend much further than is usually thought? 
Why not as high as the moon? If so, her motion 
must be influenced by it ; perhaps she is retained in 
her orbit thereby. 

This was the simple thought suggested, and it was 
this which constituted the greatest induction ever 
made in physical science. The moon is only distant 
from us some sixty times the earth's radius, and why 
should not the immense pull of the earth on all mat- 
ter near itself be felt at that distance? Of course if 
this is the force which holds the moon and the planets 
to their orbits it must, as can be proved by Kepler's 
third law, diminish with the square of the distance 
from the centre of motion. From the well known 
relations of the centre of gravity, the pull of the 
earth on all bodies near its surface, as well as its pull 



S6 METHOD OF CALCULATION. 

on distant bodies, may be regarded as proceeding 
from its centre of figure. Hence the force of the pull 
at the moon must be as much less than the pull at 
the earth's surface as the square of sixty-one is greater 
than the square of unity, that is, 3721 times less. But 
as the earth's pull is proportional to the quantity of 
matter on which it acts, so that all bodies great or 
small fall towards the earth with the same rapidly 
increasing velocity, — the moon just as fast and no 
faster than a stone under the same conditions, — we 
ought to expect that the moon, at its distance, would 
fall 3721 times more slowly than a stone near the sur- 
face. Now such a stone falls 16 feet the first second, 
and would fall if it had a chance 57,600 feet the first 
minute ; so that the moon should fall about fifteen 
and a half feet during the first minute of time. But 
how much does the moon fall? This is the next 
question which Newton asked ; and it is by no means 
so easily answered as the one we have just solved so 
readily. 

If the moon and planets have the compound mo- 
tion which Newton assigned to them, they are in the 
paradoxical condition of beginning to fall at every 
moment of time towards their primaries ; always be- 
ginning to fall but never falling. Should the earth's 
pull at any instant suddenly cease the moon would at 
once resume its primary motion of translation, start- 
ing off on a tangent with the uniform velocity which 
it had at that moment in its orbit. If now we con- 
struct in imagination an arc of the moon's orbit de- 
scribed around a centre representing the earth, with 
a tangent starting off at the point where the earth's 



FIRST RESULT UNSATISFACTORY. 8/ 

pull is assumed to stop ; and from this point of con- 
tact measure off the distance on the arc over which 
the moon actually moves in one minute ; and finally 
through the extremity of the arc thus found draw 
from the centre a radius, and extend the line until it 
intersects the tangent, — then this intersection will be 
the point which the moon would have reached in one 
minute had it started off on the tangent as assumed ; 
and the portion of the radius between the tangent and 
the arc will represent the distance through which the 
moon actually falls to the earth during this same 
minute of time. Knowing the radius of the orbit 
and the angle subtended by the arc at the centre, 
and assuming — as we may — that such a small arc 
is practically circular, it would be the simplest of 
trigonometrical problems to calculate the distance in 
question. In Newton's time, however, the calcula- 
tion involved many uncertain elements, which he 
showed great judgment in selecting and skill in com- 
bining. But the first result was unsatisfactory, for it 
appeared that the fall was only thirteen feet, instead 
of fifteen and one half feet as the theory required. 

Most men would have regarded this as at least a 
sufficient approximation to induce them to continue 
the investigation; and no circumstance indicates 
more plainly the balance of Newton's mind and the 
dispassionateness of his temperament than that he re- 
garded the result as disproof, and at once dismissed 
the theory from his thoughts. 

In a few years, however, the cause of this failure 
to verify the theory was fully explained. The cal- 
culation which Newton had made involved a know- 
7 



88 THE THEORY VERIFIED. 

ledge of the moon's distance in feet, while the 
astronomical determination of this distance depended 
on trigonometrical measurements of which the earth's 
radius was the base ; and only gave the information 
that the distance was about sixty-one times this ra- 
dius. To reduce the result to feet, it was necessary 
to know the length of the earth's radius in feet, and 
here was the difficulty. We cannot of course meas- 
ure the radius directly, but we can measure an arc 
of a meridian circle on the earth's surface, and from 
the length of an arc of known extent — say five de- 
grees — calculate the length of the radius. This is what 
Newton had done, assuming, according to the received 
estimate at the time, that one degree on the meridian 
measured sixty miles. In 167 1, however, a new 
measurement of an arc of a meridian, between Ami- 
ens and Malvoisine in France, was made by the 
astronomer Picard, which showed that the received 
length of a degree was greatly in error; and that 
instead of being sixty it was sixty-nine English stat- 
ute miles of 5280 feet each. When this result be- 
came accredited in England, Newton revised the 
calculation which had so long been laid aside ; and 
the result was an agreement with theory so exact as 
to leave no longer any doubt in his mind of the truth 
of his early conception. As the story is told by 
Robinson, " He went home, took out his old papers, 
and resumed his calculations. As they drew to a 
close he was so much agitated that he was obliged 
to desire a friend to finish them." 

This in outline is the history of the greatest scien- 
tific induction which man has ever made. In draw- 



THE INDUCTION OF NEWTON. 89 

ing the sketch, I have given prominence to those 
features which from my point of view seemed most 
essential, and have doubtless passed unnoticed facts 
and relations which others might deem more impor- 
tant. But the interaction of mind on mind, which 
scientific progress involves, is usually very complex ; 
and, in the absence of detailed information, there is 
room for great differences of opinion. It is much to 
be regretted that we have not fuller knowledge, espe- 
cially in regard to the sequence in which the various 
elements of the problem were presented to Newton's 
mind ; but he, unlike his predecessor Kepler, was very 
reticent, and did not display all the processes of his 
thoughts. 

We might, with Whewell, classify the general results 
of Newton's work under fi^ve different propositions, 
which undoubtedly came before him at one time 
or another as separate problems: first, that the 
strength of the pull of the sun on different planets 
diminishes with the square of the distance ; secondly, 
that a force so acting would cause the planet to 
move in elliptical orbits, in accordance with the first 
and second laws of Kepler; thirdly, that the earth 
so acts on the moon, and that this force is identical 
with gravity; fourthly, that this force is universal, 
causing an attraction between all bodies under all 
conditions ; fifthly, that the strength of the force 
increases in the same proportion as the combined 
weights of the attracting bodies, and may be re- 
garded as the sum of the actions of the various par- 
ticles or units of mass of which they consist. 

Such a classification is useful, as a summary of 



90 THE INDUCTION OF NEWTON. 

what has been — in great measure — already stated, 
as pointing out the separate elements of the problem, 
and as showing how great the work really was. But 
all these propositions except the third, were deduc- 
tions from known principles ; and the identity of the 
central force with gravity being granted, the rest 
necessarily followed. Not that we would in the least 
degree depreciate the skill with which these deduc- 
tions were worked out. On the contrary, as with 
every investigation, this was Newton's real work ; " hie 
labor, hoc opus est;" and it has always won, and ever 
will claim the admiration of the world. But it was 
the great induction, and not these deductions which 
we are endeavoring to illustrate. The induction was 
to a large extent — if not wholly — a spontaneous 
action of the mind ; but it is by just such action that 
the level of knowledge is raised. After any great 
induction it always requires time — it may be long 
time — to work up to the new level. It was so after 
Hipparchus ; it was so after Copernicus ; it was so 
after Kepler; and astronomy has not yet reached the 
level which Newton set. The deductions may require 
greater intellectual skill, as they necessarily involve 
incomparably greater labor; but they do not raise 
the level. As in building, it requires little work to 
raise the scaffolding, but then comes the long and 
arduous toil of the builders to prepare the walls on 
which to mount still higher. 

If gravity reaches to the tops of the highest moun- 
tains, why not as high as the moon ? This was the 
fundamental conception which led to the great result. 
Seeing how apparently trivial and accidental was the 



THE INDUCTION OF NEWTON. 9 1 

thought which bound together the universe in its all 
embracing grasp, some may imagine that the individ- 
ual merit of the conception was inconsiderable. But 
they must remember that the thought would have been 
barren without the knowledge to make it pregnant, 
or without the labor to make it real. Others, like 
Hooke and Cassini, did claim to have had the thought 
as well as Newton ; but their thought was barren, and 
the world has paid no regard to their claims. Again, 
some may think that, given the knowledge and the 
intellectual power, the thought came without observa- 
tion, and that to God and not to man belongs all the 
glory. If by this is meant that the thought came as 
an inspiration to a mind prepared to receive it, I 
should agree to the proposition; 

" For merit lives from man to man, 
And not from man, O Lord, to Thee." 

And I myself believe that just as to the intellectually 
strong and teachable there come revelations of larger 
knowledge about material things, so to the spiritually 
minded and open-hearted there comes in a similar 
way a deeper insight into the spiritual life ; and it is 
because I believe these material relations to be a 
type of the spiritual, and to have the same, though 
no more certain sanctions, and it is because I hope, 
through a more intimate knowledge of the facts, to 
aid in reconciling the two orders of truth, that I have 
dwelt so long on this instructive history. 

The character of Newton was entirely in harmony 
with his lofty career. It was marked by sedateness 
of demeanor ; soberness of conversation ; sobriety of 



92 THE CHARACTER OF NEWTON. 

conduct; persistency in effort ; devotion of will; hu- 
mility of disposition ; reverence of mind, and absorp- 
tion in thought. He never would admit there was 
any difference between himself and other men ; and 
when asked how he made his discoveries, replied, " I 
keep the subject of my inquiry constantly before me, 
and wait till the first dawning opens gradually, by 
little and Httle, into a full and clear light." It is into 
minds in such a frame that the light shines ; and by 
waiting on the Eternal Purpose the revelations of 
great truths come. 



INDUCTION RAISES THE LEVEL OF KNOWLEDGE. 93 



LECTURE IV. 

DEDUCTION. 

IN my last lecture I said that a new induction raises 
the level of human knowledge; and this figura- 
tive expression very exactly indicates the new rela- 
tions which are thus introduced into the world of 
thought. There is not simply an addition to knowl- 
edge, but the old knowledge is seen in a new light. 
Facts previously disconnected are found to be united 
by common bonds. Phenomena which appeared 
mysterious and fortuitous now appear regular and 
natural. Principles which were supposed to be fun- 
damental are found to be dependent. Partial and 
formal laws are merged in more universal and sim- 
pler modes of action. Order and harmony prevail 
where before was only confusion and discord. 

But to show what are the results of the new princi- 
ple that has been introduced, to trace all its connec- 
tions, to develop the consequences, both near and 
remote, to test by observation or experiment, the 
deductions in every detail, and to follow out the 
lines of investigation thus opened, requires a great 
amount of thought and labor, and the more in pro- 
portion as the previous induction is broader and 
more commanding. In this way the general standard 



94 DEDUCTION BROADENS KNOWLEDGE. 

of knowledge is brought up to the new level, and the 
foundations are laid on which to rise to a still more 
commanding position. It is work of this sort which 
almost exclusively occupies the time and taxes the 
energies of the great body of scientific investigators ; 
and in the economy of nature many thousand workers 
are ready to carry out the conceptions of one great 
master. 

The great originator is highly favored among men, 
but let it not be inferred that the part of his fellow- 
workers is less honorable, or their labor less difficult, 
or less necessary. Not only is it that 

"All are architects of Fate, 

Building on these walls of time," 

but it is also true that some of the greatest intellect- 
ual achievements have consisted wholly in following 
out well-established principles to their necessary con- 
sequences. Newton's great induction commands our 
highest admiration, but so do equally the deductions 
which Laplate and Lagrange and Gauss severally 
drew from Newton's all-embracing law. No work 
of science can be compared with the "Principia" in 
the effect produced on the progress of knowledge; 
but it may be questioned whether it shows as great 
intellectual power as the *' Mecanique Celeste." 

The mathematical sciences give us the most char- 
acteristic examples of the deductive method, and 
mathematics is the most important tool in such pro- 
cesses of thought. The necessity of such aid arises 
from the limited power of the human mind in com- 
bining details, in following sequences, in remember- 



ARABIC NUMBERS. 95 

ing successive steps, and in general in concentrating 
thought. The various forms of calculus help the rea- 
soning powers very much in the same way that the 
microscope, the telescope, or the telephone, aid the 
eye or the ear in observing natural phenomena. 

This fact we recognize in the simplest forms of 
mathematical calculation. The Arabic numerals, 
with the so-called decimal system of arithmetic, en- 
able any one readily to obtain results which, without 
their aid, would be attainable only by a mathematical 
genius ; and if we analyze the mental processes of 
the remarkable calculators who from time to time 
appear, we find that their wonderful ability depends 
chiefly on a vividness of memory and imagination, 
which enables them to keep before their minds, and 
thus combine, a* great number of partial results. 
Each of these by itself might have been obtained 
mentally by the average man ; but he finds it neces- 
sary to aid his memory by noting down every step 
of his calculation on slate or paper. 

Men with such a knack at figures are also able 
to combine results by quick methods which are out 
of the reach of ordinary computers ; while the com- 
mon rules of decimal arithmetic are adapted to the 
average mind, and give just the aid which will enable 
it to reach most rapidly and accurately, the required 
result. 

It may be well here to set right a common mis- 
apprehension, that the rules of arithmetic have some 
special relation to the number ten. Since Nature 
gave man ten fingers or digits, which make a very 
simple but efficient calculating engine, he instinc- 



96 DECIMAL SYSTEM. 



lively, at a very early period, distinguished and gave 
names to ten corresponding numerals, also frequently 
called digits ; but it was not until man had tried vari- 
ous clumsy expedients of combining these digits to 
express larger numbers, that some good genius, sup- 
posed to have been an Arabian, devised our simple 
method of expressing numerical values. The arith- 
metical rules are the outcome of this method, and 
would work just as well with any other number of 
digits as with ten. Eight digits would have given us 
a simpler arithmetic, and twelve digits, in many re- 
spects, a more convenient one. Such, however, is 
the force of habit and the conservatism of education 
that a change now would probably be impracticable ; 
but we cannot but regret that our early parents did 
not omit the thumbs in the first count. Eight units 
can be evenly divided three times, ten units but once ; 
and this power of successive subdivision is of para- 
mount importance in commercial transactions, as the 
experience in France with decimal weights and 
measures plainly shows.^ 

^ The truth of this statement, although really so simple, 
seems so inconsistent with our familiar habits and ordinary- 
experience, that some further illustrations of it may be desired. 
In our system of enumeration we use in addition to the zero 
mark separate signs for the first nine digits, and express all 
higher numbers by an ingenious method of combining these 
signs, or figures, as the signs are called. The system consists 
in writing the figures in a definite order on a horizontal line, 
and assigning to the digits a value increasing by powers of ten 
as we proceed from right to left. The figure in the first or 
units' place stands for single digits ; the figure in the second or 
tens' place stands for ten times the number indicated by the 



OCTUPLE SYSTEM. 9/ 

The French system of weights and measures is 
constantly advocated on account of its decimal sub- 
division, but these are a positive disadvantage. The 
one valuable feature of the French system is the 
simple relation which it establishes between measures 
and weights, and it would doubtless be a great gain 
if such a system were adopted by all nations ; but it 
would be a still greater gain if we could get rid of 

sign ; the figure in the third or hundreds' place for ten times 
ten, or one hundred times, the number indicated ; that in the 
fourth or thousandths' place for ten times ten times ten, or one 
thousand times, the number expressed ; and so on. The ex- 
pression 63,597, for example, signifies six ten thousand, added 
to three thousand, added to five hundred, added to nine tens, 
added to seven ; and we are so familiar with this method of 
enumeration that we are apt to forget how artificial it is, and 
how much we are indebted to the ingenious men of Arabia, or 
elsewhere in the East, who invented the system. 

The efficiency of this system, and the validity of the rules 
which arise under it, depend not on any peculiar virtue in the 
number ten, but simply on the mode of combining the figures 
to express values. As above said, there was no reason for 
selecting the number ten more weighty than the authority of 
the ten of fingers and the ten of toes ; and any other number 
might have been taken as the basis of the system equally well. 
For example, we might use eight as the basis of the system, and 
assign to the digits, arranged as before, values increasing by 
powers of eight. We should then discard two of our figures, 8 
and 9, and omit the corresponding names in counting, thus : — 






I 


2 


3 


4 


5 


6 


7 


8 


9 


10 


&c. 


Decimals. 





I 


2 


3 


4 


S 


6 


7 


10 


II 


12 


&c. 


Octuples. 



We might use the same names and figures for all the numbers 
up to seven ; but we should be obliged to give a wholly different 
significance to all compound numbers, while assigning to them 



98 OCTUPLE SYSTEM. 

two of our digits, and establish our system of arith- 
metic on an octonary instead of a decimal basis. 

the names we use for the corresponding compounds (not the 
corresponding numbers) on the decimal system. Thus ten 
(lo) in the octuples would have the same value as eight (8) in 
the decimals ; twenty in the octuples the same value as sixteen 
in the decimals ; one hundred in the octuples the same value 
as eight times eight, or sixty-four, in the decimals, &c. How 
completely the introduction of a new system would destroy our 
association with numbers will be evident from the following 
multiplication table on the octonary system -. — 

MULTIPLICATION TABLE. 









Octonary System. 








I 


2 


3 


4 


5 


6 


7 


10 


2 


4 


6 


ID 


12 


14 


16 


20 


3 


6 


II 


14 


17 


22 


25 


30 


4 


10 


14 


20 


24 


30 


34 


40 


5 


12 


17 


24 


31 


36 


43 


50 


6 


14 


22 


30 


Z^ 


44 


52 


60 


7 


i6 


25 


34 


43 


52 


61 


70 


10 


20 


30 


40 


50 


60 


70 


100 



Obviously, it would be impracticable for us who learned to 
cipher by the decimal system to change our habits of thought, 
and acquire a second nature under which twice four would sug- 
gest involuntarily ten, or four times six thirty, with correspond- 
ing changes in all processes of simple addition and subtraction. 
Think of the confusion of bank clerks and other lightning cal- 
culators if six and seven became fifteen, or three from ten five ! 
Nevertheless, apart from the force of habit the transition would 
be a very simple one. The fundamental operations of arithme- 
tic would not be essentially altered thereby ; and to those edu- 
cated in it the octuple system would appear as natural as the 
one we so familiarly employ. A single example will make this 
point clear. 

Let us assume that we have two numbers 234 and 345 writ- 
ten on the octuple system to multiply together. We proceed 



OCTUPLE SYSTEM. 99 



Although this digression has no immediate bearing 
on our subject, it shows how conventional our system 

exactly as we should on the decimal system only using the new 
multiplication table, and making the corresponding addidons, 
thus : — 

234 156 

345 229 

14 14 1404 

1160 312 

724 312 

105,614 35,724 

We read the two numbers two hundred and thirty- four and 
three hundred and forty-five, and the product one hundred and 
five thousand six hundred and fourteen just as we should on 
the decimal system. But on the octuple system the same num- 
bers express wholly different values. These values, however, 
can be readily reduced to the decimal basis, if we remember 
that on this basis the value of the successive places in the oc- 
tuple enumeration increase by powers of eight. Hence, the 
value of 234 in octuples would be found in decimals thus : — 



Octuples. 
200 = 
30 = 


2 
3 


X 8 X 8 
X 8 


Decimals. 
= 128 
= 24 


4 = 






= 4 



234 156 

So also the value of 345 in octuples would be found : — 

300 = 3 X 8 X 8 = 192 

40 = 4 X 8 =32 

5 = = 5 

345 229 

The product of 156 by 229 decimals has already been found 
above to be 35,724, and we can now prove that the ordinary rule 
of multiplication apolies to octuples as well as to decimals, by 



100 MATHEMATICS AIDS DEDUCTION. 

of arithmetic really is, and what an efficient aid it is 
in our mental processes. 

As we go forward in the study of mathematical 
subjects the more necessary does the aid furnished 
by mathematical symbols become, and we very soon 
reach a point where even the most gifted intellect 
cannot dispense with their arbitrary forms. They 
enable the mind to combine conditions and see rela- 
tions which otherwise it could not possibly grasp. 
Hence it is that every great improvement in math- 
ematical methods has always been followed by a 
great extension in our knowledge of material re- 
lations; new deductions from old principles have 
become possible, and thus knowledge has been broad- 
ened and the way made ready for larger inductions. 

showing that this product is the exact equivalent of the octuple 
product 105,614 also before obtained by following the regular 
arithmetical rule, of course using the octuple multiplication 
table and the corresponding octuple additions as before de- 
scribed. 

Octuples. Decimals, 

icoooo =1X8X8X8X8X8 = 32768 

5000 =5X8X8X8 = 2560 

600 = 6 X 8 X 8 =384 

10 = I X 8 =8 

4 = =4 



105,614= =3S>724 

The same point could be illustrated by other arithmetical oper- 
ations ; but the above example is sufficient to enforce the state- 
ment made above ; and it must now be evident that the great 
merit of what we wrongly call "decimal" arithmetic depends on 
the system of Arabic numerals, and not at all on the number of 
digits it employs. 



SCIENCE OF QUANTITATIVE RELATIONS. 10 1 

It was SO when the Cartesian geometry gave a knowl- 
edge of the properties and relations of curved lines 
and surfaces before unsuspected. It was so when 
Newton and Leibnitz invented general methods of 
dealing with the so-called infinitesimal quantities of 
algebra and geometry, which led at once to the suc- 
cessful solution of the problem of central forces. It 
was so again, after Newton's death, when the conse- 
quences of the law of gravitation were developed in 
proportion as the resources of the new calculus were 
enlarged by the great mathematicians of the eight- 
eenth century, — such men as Euler, Laplace, and 
Lagrange. 

Mathematics, however, is a great deal more than 
an instrument for deductive reasoning. Just as logic 
has loftier aims than merely to dissect arguments and 
to lay bare their syllogistic forms and becomes in its 
larger expressions the science of thought, so math- 
ematics is the science of quantitative relations wholly 
independent of their material expressions; and the 
so-called multiple algebra of our own day has been 
developed far beyond our positive knowledge of ma- 
terial relations, and it is at this moment waiting for 
some higher induction or broader generalization to 
open new worlds to conquer. Indeed, so transcen- 
dental are the abstractions involved that few educated 
men, not mathematical specialists, are able to follow 
them ; although in some curious works of fiction at- 
tempts have been made to show the possibilities of 
conceiving of extension in more than three dimen- 
sions. In less abstract relations, on the other hand, 
mathematical analysis has not yet satisfied the de- 



102 SYMBOLICAL LANGUAGE OF CHEMISTRY. 

mands of existing physical problems ; and more 
satisfactory and exhaustive methods of solving equa- 
tions of higher degrees would enable the physicists 
to broaden their deductions in many directions. 

To a limited extent the symbolical language of 
chemistry may be used like mathematical formulae, 
and has a similar value in facilitating deduction. 
But its terms have a far more restricted meaning, 
and are therefore less general; and moreover, the 
chemical formulae, which we call reactions, only ex- 
press the very simple relations of combination and 
decomposition. 

As the use of the symbolical notation of chemistry 
is for the most part restricted to chemical students, a 
brief description of the system may be necessary in 
order to render the statement just made generally 
intelligible. 

We recognize at the present time about seventy 
well-defined elementary substances, and in addition 
to these there are several others whose authenticity 
has not yet been satisfactorily established. From 
these elementary substances all known materials can 
be formed; and into these the various substances 
which exist on the surface of the earth can be re- 
solved by processes with which all chemists are 
familiar. Moreover, when these elementary sub- 
stances unite to form compound bodies, the combi- 
nation takes place in certain definite proportions by 
weight. 

The modern theory of chemistry, which we shall 
have occasion to discuss more at length hereafter, 
assumes that each elementary substance is an aggre- 



103 



gate of exceedingly minute particles, called atoms, 
which "are indivisible by any chemical means now 
known, and which are alike in every respect. Thus 
a mass of the elementary substance sulphur is an 
aggregate of atoms, all of which are exactly alike, 
but wholly different from the atoms of any other 
elementary substance. These atoms, being definite 
masses of matter, must have definite weights ; all the 
atoms of sulphur, for example, absolutely the same 
weight, but a very different weight from that of the 
atoms of iron or from that of the atoms of oxygen, 
two other elementary substances. 

If the mental concepts we call atoms are really 
entities, they must have a degree of minuteness 
which vastly surpasses our powers of observation. 
Granting the existence of such minute particles, there 
are known facts of physics and chemistry which com- 
pel us to assign limits to their magnitude on either 
side ; and Sir William Thomson has estimated that if 
a drop of water were magnified to the size of the 
world, the atoms of which it consists would certainly 
appear larger than boys' marbles, and with equal 
certainty smaller than cricket balls. The almost in- 
conceivable minuteness of the assumed atoms is, 
however, in itself no weighty argument against the 
atomic theory ; for in a universe in which we recog- 
nize the infinitely great, why should we not expect to 
find also the infinitely small? If there be a macro- 
cosmos around us, why should not there be also a 
microcosmos? And if creation be not limited by the 
powers of the telescope, why should it be limited by 
the powers of the microscope? The proof of the 



104 ATOMS AND MOLKCULEs^. 

existence of atoms is solely a question of sufficient 
evidence, and may be reached in time; but as yet 
they can only be regarded as postulates of our scien- 
tific systems, the ultimate material units out of which 
the mind seeks to construct masses of matter. To 
our crude conceptions they are the bricks, as it were, 
of the material universe. 

According to the atomic theory, when elementary 
substances combine, the union takes place between 
the atoms ; and the groups of atoms thus formed are 
called molecules, and only like molecules aggregate 
together to form masses of different substances. Thus 
when oxygen gas unites with hydrogen gas to form 
water, one atom of oxygen unites with two atoms 
of hydrogen to form one molecule of water; and a 
drop of water is simply an aggregate of molecules 
of this kind, so numerous that they can only be 
counted when all the sands of the earth have been 
numbered ; but all these molecules are exactly alike, 
each consisting of two atoms of hydrogen and one 
of oxygen. 

If the atoms have definite weights, such a combi- 
nation as we have just described must take place in 
the definite proportions of these weights. As the 
combined weight of two atoms of hydrogen is to the 
weight of one atom of oxygen, so and in just this 
proportion by weight must hydrogen gas combine 
with oxygen gas to form water ; and the same gen- 
eral principle must hold in the combination of all 
other atoms, and in the production of all other com- 
pounds. Hence, according to the atomic theory, the 
combining proportions of chemistry are simply the 



COMBINING PROPORTIONS OF CHEMISTRY. 10$ 

relative weights of the atoms. Obviously, then, we 
can infer from the combining weights of the ele- 
mentary substances, which can be accurately ob- 
served, the relative weights of those abstract units 
we call atoms; and in our modern chemistry the 
combining proportions of the elementary substances 
are called, under certain limitations, the atomic 
weights of the chemical elements. The smallest of 
these weights is the weight of the atom of hydrogen, 
which we take as the unit of the system. The atom 
of oxygen weighs sixteen of these units ; the atom of 
sulphur thirty-two ; and the atom of iron fifty-six of 
the same units. In general, the atomic weight of an 
elementary substance indicates how many times the 
atoms of which it consists weigh more than the 
atoms of hydrogen. 

And here it must not be forgotten that although 
the atoms are wholly theoretical concepts, these rela- 
tive weights are definite facts of observation ; and, as 
already stated, are deduced directly from the definite 
proportions in which the elementary substances are 
known to combine. These values are independent 
of the atomic theory ; but we can most easily make 
the facts intelligible in the terms of this theory, for 
the theory gives to the phenomena a concrete expres- 
sion, and thus enables us to relate them to the rest of 
our knowledge. 

If we know the number of atoms of each kind 
which enter into the composition of a molecule of 
any substance, we can find the weight of that mole- 
cule by simply adding the weights of the several 
atoms. Thus a molecule of water, consisting of one 



I06 EXAMPLES OF CHEMICAL SYMBOLS. 

atom of oxygen and two atoms of hydrogen, must 
weigh 16 + 2 = i8. 

Now it will be obvious that if we arbitrarily select 
a symbol to stand for an atom of each element, we 
can readily represent the molecule of any substance 
whose composition is known, by simply writing to- 
gether these symbols like letters in a word. 

In our text-books of chemistry you will find a table 
giving, after the name of each elementary substance, 
the symbol which has been selected to represent its 
atom, and also the value of the atomic weight. Thus 
the atom of hydrogen is represented by H ; and its 
atomic weight, as we have said, is the unit of the sys- 
tem. The atom of oxygen is represented by O, and 
its atomic weight is 16. The atom of carbon is rep- 
resented by C, and its atomic weight is 12. The atom 
of nitrogen is represented by N, and its atomic weight 
is 14. 

We represent, then, a molecule of water by H2O, 
thus indicating that this molecule consists of two 
atoms of hydrogen and one atom of oxygen, as just 
stated; also indicating, further, that the weight of 
this molecule is 16 -\- 2 =. 18; and still further show- 
ing that in water oxygen and hydrogen are united in 
the proportions by weight of 16: 2. 

In like manner we represent a molecule of carbonic 
acid gas by CO2, a symbol which indicates, first, that 
the molecule of carbonic acid gas consists of one 
atom of carbon and two atoms of oxygen ; secondly, 
that the weight of the molecule isi2-t-2Xi6=44; 
thirdly, that in carbonic acid gas carbon and oxy- 
gen are combined in the proportion of 12 : 32. 



CHEMICAL REACTIONS. 10/ 

We call these groups the symbols of the different 
substances. 

Every chemical process may be regarded as the 
breaking up of the molecules of one or more sub- 
stances into atoms, and the regrouping of these same 
atoms to form the molecules of new substances. In 
chemistry we technically call such processes reac- 
tions; the substances which concur in the process 
we call the factors, and the substances formed by the 
process we call the products of the reaction. As no 
atom can be destroyed, every atom coming from the 
factors, and none others, must be found among the 
products ; and hence the total weight of the products 
must be exactly equal to the total weights of the 
factors. Therefore we can represent such processes 
by equations, writing on the left-hand side of the 
equation mark the symbols of the several factors 
connected by the sign of addition, and on the right- 
hand side the symbols of the products in a similar 
way. A few illustrations will make clear the meaning 
of such expressions. 

Grape Sugar. Alcohol. Carbonic Acid Gas. 

CeHi^Oe = aC^HeO + 200^ 

This reaction expresses the well-known fact that in 
fermentation grape sugar breaks up into alcohol and 
carbonic acid gas. The one factor is the symbol of 
a molecule of grape sugar. This single molecule 
yields two molecules of alcohol and two molecules of 
carbonic acid gas, or four molecules in all. Notice 
how we write two molecules of alcohol, using figures 
to express several molecules, like coefficients in alge- 



I08 CHEMICAL REACTIONS. 

bra ; and notice also that there are as many atoms of 
each elementary substance in the one molecule of the 
single factor grape sugar, as in the two molecules of 
alcohol and the two molecules of carbonic acid result- 
ing from the decomposition. 

Nitrate of Ammonia. Nitrous Oxide. Water. 

N2H4O3 = N2O + 2H2O 

(2Xi4)+4+(3Xi6)=8o (2Xi4)+i6=44 2(2+16) =36 

The second reaction expresses that the salt nitrate 
of ammonia yields, when heated, nitrous oxide gas 
and water. Here, as before, the atoms of the one 
molecule which is the factor of the reaction break 
apart, and rearrange themselves to form one molecule 
of nitrous oxide gas and two molecules of water. 
Since the symbols stand for definite relative weights, 
the reaction informs us further that from eighty parts 
of the salt we obtain forty-four parts of nitrous oxide 
gas and thirty-six parts of water. 

Dilute Sulphuric Acid. Zinc. Zinc Sulphate. Hydrogen Gas. 

(HaSO^+Aq.) + Zn = (ZiiS04 + Aq.) + Hg 

The third reaction represents the process by which 
hydrogen gas is made from dilute sulphuric acid and 
zinc. It gives in general, in regard to this chemical 
change, information similar to that we have learned 
from the two preceding examples. Moreover, it 
shows that the change consists essentially in this : 
that the atom of zinc replaces the two atoms of 
hydrogen in the acid ; when these hydrogen atoms 
pair together to form molecules of hydrogen gas. 
It will be unnecessary for my present purpose to 



VALUE OF CHEMICAL SYMBOLS. IO9 

dwell on other and more abstruse points of significa- 
tion which this symbolical language conveys. It is 
sufficient if I have made clear the more obvious 
meaning and prepared the way for a further inference, 
which can easily be drawn from the principles of the 
system which have been thus far explained. 

It can now easily be seen that this symbolical 
notation gives an admirable basis for classifying 
chemical compounds ; and further that it brings out 
analogies and enables us to draw inferences which 
otherwise would never have been suggested. If one 
substance undergoes certain changes it is probable 
that an allied substance, having a similar constitution 
and therefore represented by a like symbol, would 
partake of similar changes; and the analogy sug- 
gested by the symbols often leads us to test our in- 
ferences by experiment, and thus we are constantly 
led to the discovery of new truths. 

There is, however, a most important difference 
between a chemical reaction and a mathematical 
equation, which should be always kept in mind. 
From a mathematical equation any result that can 
be deduced by the principles of algebra must in some 
sense be true. But in chemistry we have discovered 
no such far-reaching principles; and our chemical 
reactions merely express the known facts in regard 
to each process they represent ; and we can draw no 
certain conclusions one step removed from the facts 
which the symbols signify. The notation is fruitful 
in suggestions, nothing more. 

When the laws which govern the grouping of 
chemical atoms have been formulated we may hope 



no THE SYLLOGISM. 



for an all-embracing calculus of chemical operations ; 
but from want of precise and exhaustive knowledge 
of these principles, all attempts in this direction have 
been thus far failures. Nevertheless, the conven- 
tional symbolism of chemistry has been of the very 
greatest value in suggesting possible relations and 
pointing out fruitful lines of investigation. 

Of most subjects the fundamental conceptions and 
processes do not admit of more precise designations 
than ordinary language affords, and the arguments 
which arise are discussed under the conditions which 
the science of logic seeks to analyze and classify in 
the various forms of the syllogism. We may often 
thus arrive at as complete certainty as by mathemat- 
ics, — although it is important not to wander far from 
the boundaries of known truth, and to verify every 
step of our progress by an appeal to observation or 
experiment. But whether the conclusions be reached 
by mathematical, chemical, or syllogistic reasoning, 
the method is essentially deductive; and implicitly 
the results were involved in the premises with which 
we started. 

No fountain can rise higher than its source, and 
no process of reasoning, however conducted, can 
mount above the general principles or fundamental 
truths on which the reasoning rests. These are the 
essential conditions or premises of the mental pro- 
cess, and necessarily imply previous generalizations 
which were acquired by induction. While, however, 
we admit that the results of deductive reasoning, 
however conducted, were implicitly contained in the 
data of the calculation or the premises of the argu- 



DEDUCTIONS MUST BE TESTED. Ill 

ment, we must not infer that knowledge cannot be 
increased by such means. 

Before an Infinite Intelligence all the relations of 
truth must be open ; but how far this is from being 
possible to a finite intelligence we have all sadly ex- 
perienced ; and to man the deductions of science are 
as much new truths as if they were direct revelations ; 
and the greatest discoveries have been made by 
strictly deductive processes of investigation. Indeed, 
as I have already said, knowledge is enlarged chiefly 
by deductive reasoning, verified by observation and 
experiment. Nevertheless, as has also been said, de- 
duction implies previous induction, and differs from 
induction, not in that its results are less real or less 
novel to men, but in that they are of a different 
order, and sustain different relations. What this dif- 
ference is, we shall still further endeavor to illustrate. 

If a general principle, like the law of gravitation, 
is absolutely true, everything that can be deduced 
from it by legitimate processes must be equally true. 
But in science we have constantly to deal with induc- 
tions which are only partial truths. Under such 
circumstances, entire reHance cannot be placed on 
the deductions ; and hence the importance of testing 
each step of the argument by observation or experi- 
ment. In proportion as the predictions are verified, 
the greater confidence do we place in the universality 
of the principle on which the deductions were based. 

Excepting, however, the axioms of mathematics, 
the laws of motion, and a few similar principles, there 
are no generalizations which can be regarded as ab- 
solutely beyond question ; and it is conceivable that 



112 CAUSES OF UNCERTAINTY. 

conditions may arise under which even the law of 
gravitation will fail. It is, therefore, only in pure 
mathematics and in simple physical problems, that 
we can feel safe in our deductions without submitting 
them to the test of experience. 

Uncertainty in regard to the results of deduction 
may arise, not only from failure in the particular case 
of the general principle on which dependence has 
been placed, but also from inherent difficulties in the 
deductive process. In algebra, mathematicians have 
not been able, except in special cases, to obtain com- 
plete solutions of equations of higher degrees than 
the fourth, and the ingenious methods which they 
employ with problems which give equations of a 
higher order, yield at best only partial solutions. So 
also in chemistry, the methods of analysis give only 
approximate results, and for this reason the conclu- 
sions based upon them are more or less indefinite. 
Hence arises the importance, in all physical science, 
of the discussion of what is called the probable error 
of observations, and also of the personal error of the 
observer ; and in this connection a few words on the 
errors which are inherent in all scientific methods, 
and necessarily affect their results, will not be out of 
place. 

Even among scholars, who while familiar with ,the 
general results of science are strangers to its methods, 
there is a common misapprehension in regard to the 
certainty of scientific conclusions, or in regard to the 
infallibility of scientific evidence. Physical science 
is constantly spoken of as exact, and as yielding pos- 
itive proofs, in contrast with the moral sciences, whose 



MEASUREMENTS NEVER ABSOLUTELY EXACT. II3 

results are less definite and more questionable. As 
regards physical science all this is to a great extent 
true, — since a large mass of the facts which have been 
estabHshed in relation to the phenomena of nature 
are as certain as the axioms of geometry ; but no re- 
sults of measurements are absolutely exact, and the 
accredited values have every possible degree of pre- 
cision. There are very few magnitudes of nature 
which are known accurately within a thousandth part 
of their value ; and our knowledge of such funda- 
mental quantities is often in error to the extent of 
one-tenth. To scientific experts this is a familiar 
fact, and in all their deductions they take into ac- 
count the resulting uncertainty ; but literary men are 
apt to reason as if they thought everything accepted 
in science was known with equal exactness, and are 
led into error by this unconscious assumption. A 
very small experience with the reality would dispel 
this illusion ; and hence the Importance to all scholars 
of that limited experience with scientific methods 
which will give an understanding, not only of the true 
relations of scientific facts, but also of the limitations 
of scientific results. 

The unavoidable errors of scientific methods may 
be classed under two heads; and we must distin- 
guish the constant errors, which are inherent in the 
process employed or in the observer himself, from 
the accidental errors, which are determined solely by 
chance. The last are as likely to be In one direction 
as another; while the first, under the same conditions, 
are always in the same direction. 

Of the two classes of errors the accidental errors 



114 ACCIDENTAL ERRORS. 

are by far the less important, and to a great extent 
can be eliminated by multiplying observations. The 
arithmetical mean of several observations is always 
far more trustworthy than any single observation, 
and the theory of probabilities gives us in such 
cases a method of estimating, not only the probable 
error of any one observation of the set, but also the 
probable error of the mathematical mean. The dis- 
cussion of probable errors is one of the most impor- 
tant applications of mathematics, which is generally 
known as the " Method of Least Squares ; " and it is 
certainly a most remarkable result of science that what 
would seem to be at first sight so wholly accidental 
and utterly lawless, should be found to be regulated 
by definite principles and become a matter of exact 
computation. Yet this is strictly true. If, for ex- 
ample, we first eliminate from a series of observa- 
tions of some definite quantity, as for example the 
value of an angle, all evident mistakes and known 
causes of error, there will still remain differences in 
the results, which will appear the more pronounced 
in proportion as we seek to secure greater accuracy 
in our measurements. Such differences we call acci- 
dental errors, and they are due to numberless causes 
which we cannot estimate, depending upon the im- 
perfection of our instruments, or of our senses, or on 
the varying conditions under which all experiments 
must be made. Now if we take the arithmetical 
mean of all the numbers obtained as the most prob- 
able value, and call the difference between the mean 
value and each separate value the error of that 
observation, it will always appear, — 



"PROBABLE ERROR." II5 

First, that small errors are more frequent than 
large ones. 

Secondly, that positive and negative errors are 
equally frequent. 

Thirdly, that very large errors do not occur. 



Observations. 


V. 


Z/2. 


/ // 






116 43 44.45 


5.19 


26.94 


50.55 


—0.91 


0.83 


50.9s 


— I-3I 


1.72 


48.90 


0.74 


0.55 


49.20 


0.44 


0.19 


48.85 


0.79 


0.63 


47.40 


2.24 


5-02 


47-75 


1.89 


3.57 


51.05 


— 1.41 


2.00 


47-85 


1-79 


3-20 


50.60 


— 0.96 


0.92 


48.45 


1. 19 


1.42 


51-75 


—2. 1 1 


4-45 


49.00 


0.64 


0.41 


52-35 


—2.71 


7-34 


51.05 


— 1.41 


2.00 


51.70 


—2.06 


4.24 


49.05 


0.59 


0.35 


50-55 


— 0.91 


0.83 


49.25 


0.39 


0.15 


46.75 


2.89 


8.35 


49.25 


0.39 


0.15 


53-40 


-3.76 


14.14 


51-30 


—1.66 


2-75 


= ii6°43'49"-64 


;2 = 24 


2 2/2 = 92.15 


.;- 0.6745 ^^'^•;5_ 


i-''35 


-=vi=° 



On these fundamental principles derived from ex- 
perience all our reasoning on the subject is based. 



Il6 CONSTANT ERROR. 



An examination of tables of observations, such as are 
given in the Reports of our Coast Survey, may be 
very instructive as they exhibit in a most remarkable 
manner the principles we have been endeavoring to 
illustrate. 

Thus, in a series of twenty-four measurements of 
an angle of the primary triangulation made at the 
station Pocasset in Massachusetts, and cited on the 
previous page, all the above principles are strikingly 
illustrated; and it further appears that while the 
largest difference from the mean value amounts to 
5". 19, the probable error of a single observation is 
but i".35, and the probable error of the mean value 
only o".28. The term " probable error," as thus used, 
has a conventional meaning, and simply signifies 
that there is an even chance that the true value is 
within the limit assigned. 

But while such accidental errors as have been de- 
scribed are constantly reminding us of the restric- 
tions of our powers, they are limited in extent, and 
as also we have seen, can be to a large extent elim- 
inated. Not so with the constant errors which arise 
from unknown causes of various kinds, or even from 
the idiosyncrasies of the observers. These may be 
very large, are likely to operate only in one direc- 
tion, and may thus seriously vitiate our results. 
They are an insidious foe against which all our 
watchfulness and care cannot protect us, an enemy 
in the dark, of whose direction and magnitude we 
can form no estimate. These constant errors are 
the chief source of difficulty in all experimental 
investigation ; they have occasioned incalculable loss 



CONSTANT ERROR. 11/ 

of labor; and besides discouraging the investigator, 
they frequently introduce an element of uncertainty 
into his results. Years of conscientious and careful 
investigation have thus been rendered unavailing by 
an unsuspected error which has vitiated the whole 
work ; and values which had been regarded as among 
the best-estabhshed data of science have subsequently 
been found to be erroneous, owing to the discovery of 
a source of error in the method by which they were 
determined. A remarkable example from my own 
experience will illustrate these important points. 

The atomic weights are among the most important 
constants of science, and the accurate determination 
of these numerical values involves analytical work of 
great refinement and accuracy. In 1856 Schneider, 
of Berlin, made a determination of the atomic weight 
of antimony, and obtained the number 120.3. The 
work was done with all the skill and precision that a 
master of analytical chemistry could devise, and every 
known and conceivable cause of error appeared to 
have been foreseen and allowed for. Eight separate 
determinations were made, no one of which differed 
from the extreme value more than 0.23. Neverthe- 
less, a year later Mr. W. P. Dexter, working with a 
different method, but with equal refinement, obtained 
as a mean of ten determinations 122.34, that is, a value 
two whole units greater than the first, — although here 
again the results of the several determinations agreed 
so closely with each other that the maximum differ- 
ence from the mean value was only 0.14. At very 
nearly the same time the famous chemist Dumas 
made at Paris still a third independent determination 



Il8 CONSTANT ERROR. 

of the constant under consideration, using a wholly- 
different method from either Schneider or Dexter, 
and obtained 122.00, — nearly the same value as Dex- 
ter, and with a similar close agreement between the 
results of four separate experiments. The deserved 
reputation of Dumas for accuracy, skill, and judgment 
gave such authority to his result that it was at once 
adopted, and remained for twenty years the accepted 
value of the atomic weight of antimony. 

In 1877 I was myself led to repeat the determina- 
tion of Schneider, only reversing his processes, and 
obtained very closely his value of about 120. This 
led me to repeat the process of Dumas, when I ob- 
tained a still closer confirmation of the larger number, 
122. What could be the occasion of this large differ- 
ence? The discrepancy could not arise from the 
ordinary errors of analytical work, which in either 
process was far less than this ; as the close agreement 
of the separate results obtained by the same process 
plainly showed. There must be some unknown con- 
stant error affecting one or both of the results. To 
confirm this conclusion I made a third determination 
of the atomic weight, by a process which had never 
been employed before and which admitted of great 
accuracy. This gave me with great exactness the 
first value, 120; and when a fourth determination 
by still another process also gave the same value, I 
felt convinced that the higher number, which had 
been so long accepted, was the one which had been 
affected by the constant error, but I did not feel sat- 
isfied until I detected the cause of the error and 
showed in what it consisted. 



COINCIDENCES MAY BE ILLUSORY. II9 

This experience is a fair illustration of what is con- 
stantly met with in scientific investigation, and indi- 
cates moreover the only general method of ferreting 
out constant errors. When determinations of a given 
value made by essentially different methods are ac- 
cordant, we have a well-grounded confidence in their 
accuracy; but mere coincidences of numbers obtained 
in the same way are no proof of truthfulness, for con- 
stancy of results often arises from constancy of errors. 
I would that I could convey to you the full force of 
the impression which is left on the mind after repeated 
experiences such as I have described. The helpless- 
ness which one feels while thus working in the dark 
gives a reality to the sense of the limitations of our 
knowledge, of which so much is said and so little 
appreciated. If anything will lead man to hold his 
knowledge in humility and reverence it is the con- 
sciousness that results so laboriously obtained may 
be invalidated by circumstances over which he has 
no control, and of whose existence he is wholly 
unaware. 

I would that I could also give an adequate concep- 
tion of the great amount of conscientious work which 
is expended on the deductions of science for the sole 
love of truth. Were it possible, I am sure that your 
respect for the scientific investigator would be greatly 
increased and your belief in his sincerity established, 
however mistaken you may at times deem his opin- 
ions or his judgment. Of course in the cultivation 
of science, as in every other pursuit of life there is 
abundant room for the display of unworthy motives 
and ignoble passions ; but I venture to assert that 
9 



120 COMPLEXITY OF NATURAL PHENOMENA. 

there is no class of men in the world among whom is 
found more unselfish devotion and more personal sac- 
rifice than among the great army of scientific workers. 
The love of abstract truth may be a much lower 
motive than the love of man, but it equally calls 
forth the very noblest qualities of the mind. More- 
over, in most cases the constancy and courage of the 
scientific investigator meet with no reward except 
the satisfaction which unselfish duty conscientiously 
discharged always brings; and, as Professor Tyndall 
has said, ** There is a morality brought to bear on 
such matters which in point of severity is probably 
without a parallel in any other domain of intellectual 
action." 

The difficulties of scientific deduction are further 
vastly increased by the circumstance that in the 
phenomena of nature the effects of various causes are 
usually so correlated and intertwined that the task of 
separating them or of determining their precise rela- 
tions is well-nigh hopeless. Take such an apparently 
simple phenomenon as the rise of the column of mer- 
cury in the stem of such a thermometer as is univer- 
sally used to measure changes of temperature. The 
height of the mercury column depends on a number 
of causes which combine to produce the result we 
observe. Besides slight effects arising from mechani- 
cal strain or irregularities of the tube, we must distin- 
guish, first, the expansion of the mercury, of which 
the rate slowly increases as the temperature rises, 
and which tends to raise the column ; secondly, the 
expansion of the glass, which is very irregular and 
tends to depress the column ; thirdly, certain obscure 



ILLUSTRATED BY THE THERMOMETER. 121 

changes in the texture of the glass itself which act 
slowly, but which on the whole tend slightly to raise 
the column. It is true that the last two effects are so 
inconsiderable as compared with the first that they do 
not seriously interfere with the use of the instrument 
as a rough measure of temperature in our houses. 
But when in scientific investigation we seek an exact 
measure, to the hundredth of a centigrade degree, 
they interfere most seriously ; so that while small dif- 
ferences of temperature may be thus closely estimated 
under restricted conditions, we have no means of meas- 
uring large changes of temperature with any such 
approach to exactness; and beyond a certain limit 
of accuracy the use of this simple instrument is one 
of the difficult problems of science. Even in the 
ordinary use of the thermometer for determining the 
temperature of the external air, very considerable 
differences may be caused by radiation, from the 
ground, from the sky, or from surrounding objects, 
depending on the exposure of the instrument; and 
the discrepancies between neighbors on the state of 
the weather — which are often so amusingly paraded 
— are simple illustrations of what is very familiar to 
every scientific observer. 

If, now, instead of using the thermometer as a 
measure of temperature, we seek to estimate each of 
the separate effects whose combined action the in- 
strument registers, we are met at once with almost 
insuperable difficulties, and the approximate solution 
of this problem by Regnault was one of the triumphs 
of experimental science. By an ingenious method of 
experimenting, first devised by Dulong and Petit, he 



122 ILLUSTRATED BY THE BAROMETER. 

succeeded in measuring the absolute expansion of 
mercury, and when this was known he could estimate 
the expansion of the bulb and tube of which the 
thermometer was made. 

As with the thermometer, so again with the barom- 
eter. The height of the mercury column in the 
barometer depends not only on the pressure of the 
air which the instrument is intended to measure, but 
is also perceptibly influenced by a variety of other 
causes, such as temperature, the force of gravity, and 
capillary attraction. For some of these effects we 
can make accurate corrections, but for others we can- 
not ; so that the readings of a barometer made with 
the greatest refinement at Paris, are not strictly com- 
parable with those of one made with equal care at 
New York ; and the only way in which we could 
make an exact comparison would be by transport- 
ing the same instrument to and fro between the two 
places, as we might a metre measure. 

These are but two examples of a universal experi- 
ence. All the phenomena which we attempt to 
observe are obscured by other phenomena with which 
they are associated, and all the instruments with 
which we make our measurements are more or less 
fallible and faulty. Hence the general principles we 
deduce from our observations partake of the same 
limitations. This is no hair-splitting metaphysical 
refinement ; for, with the exception of a few of the 
great primary principles of nature, like the law of 
gravitation or the conservation of energy, there is 
hardly one of the so-called laws of physics or chem- 
istry which we should implicitly trust in circum- 



LIMITATIONS OF HUMAN FACULTIES. 1 23 

Stances widely differing from those under which they 
are established. As a rule, mathematical deductions 
are based not on actual qualities of bodies, but on 
ideal relations which have no exact material repre- 
sentatives. There are no such things as the rigid 
bars, the simple pendulums, and perfect fluids of our 
theoretical mechanics. These are as much abstrac- 
tions as are points, lines, and surfaces ; and in many 
respects the sciences of mechanics and astronomy are 
as much products of pure thought as geometry. 

In order to bring the problems suggested by nature 
within the grasp of his analysis, the mathematician is 
forced to simplify them by leaving out of considera- 
tion every accessory circumstance. As the late Stan- 
ley Jevons has so strikingly said in his " Principles 
of Science," ** The faculties of the human mind, even 
when aided by the wonderful powers of abbreviation 
conferred by analytical methods, are utterly unable 
to cope with the complications of any one real prob- 
lem." Of course the mathematician endeavors to 
approach the natural problem as nearly as possible, 
and in most cases the differeifces do not alter essen- 
tially the character of the solution within reasonable 
limits ; but they do narrow, and often most seriously, 
the scope of the deductions. 

Many educated men who are familiar with the 
great definiteness of the elementary mathematics, 
form an exaggerated conception of the power and 
infallibility of mathematical analysis ; and from their 
limited observation infer that mathematics has the 
power of solving, in a perfect manner, all problems 
which involve only quantitative relations. And when 



124 LIMITATIONS OF MATHEMATICAL ANALYSIS. 

we consider what they have accomplished, the powers 
of such minds as those of Lagrange and Laplace do 
appear almost miraculous. But when we compare 
the simple problems which they have solved with 
the complicated relations which modern investigation 
has revealed, even the powers of such masters are 
seen to be inadequate ; and to follow out the deduc- 
tions from principles already known, appears to be a 
hopeless undertaking. 

Jevons, whom we have just quoted, also says 
that '' if a mathematical problem were selected by 
pure chance out of the whole variety which might be 
proposed, the probability is infinitely slight that a 
human mathematician could solve it." Let me cite 
a famihar instance. 

The undulatory theory of light presents relations 
peculiarly favorable to mathematical analysis, and 
from which a great wealth of deductions has been 
drawn. But the colors of the rainbow, or more gen- 
erally the whole range of phenomena attending the 
dispersion of light by refracting media, still remain 
essentially unexplained ; and the most that Cauchy — 
perhaps the ablest mathematician of this century — 
was able to accomplish was to show that under 
certain assumed circumstances such a result might 
follow from the undulatory theory, and to make evi- 
dent that the complete solution of the problem was 
beyond our present powers of mathematical analysis. 

So also in regard to the finality of mathematical 
deductions. It is a common remark that figures 
cannot lie; but, as many have found to their cost, 
they may be made to bewilder the ignorant and 



LIMITATIONS OF MATHEMATICAL ANALYSIS. 1 25 

cover up a great deal of error. Mathematical results 
are conclusive only as regards the assumed relations 
with which the analysis starts ; and these may be so 
different from the relations of any real problem of 
nature as to render the conclusions inapplicable in 
any specific case. 

It should be clearly understood that there is noth- 
ing mysterious about mathematics ; that even when 
its processes cannot be followed except by adepts, 
its premises and conclusions can always be clearly 
stated. The operations or processes of thought 
which it combines by means of its admirable sym- 
bolism, are severally perfectly intelligible ; but in the 
multiplicity of the possible relations confusion may 
readily arise, and it requires a keen intellect, with 
great power of abstraction and concentration, to trace 
out these relations to their consequences. Without 
the symbols the task would have been beyond the 
best human faculties, except in the simplest prob- 
lems ; and even with all the aids which an ingenious 
symbolism can give, the power of combination is 
very limited and wholly inadequate to grasp the 
complex relations which the real phenomena of 
nature invariably present. 

In thus dwelling on the limitations of scientific 
deductions, I am not overlooking its grand results. 
These last speak for themselves, and are fully appre- 
ciated and honored. They have become an impor- 
tant element of our daily life, and have profoundly 
modified the thought of our time ; and while we are 
thankful for the acquisitions of the past, we look for 
still greater rewards in the near future. It is well, 



126 RESERVE OF SCIENCE. 

however, at times, instead of looking back at what 
has been done, to look forward to what remains to 
be accomplished, and to compare our knowledge, not 
with what our fathers knew, but with the universe 
about us. Courage, enterprise, and confidence are 
great virtues, but so are also modesty, caution, and 
reservation of judgment. When men venture to 
frame theories of creation and claim that the existing 
order might have resulted from the principles of 
action now known, I am at a loss which most to 
admire, their unconsciousness or their boldness. My 
only attempt at refutation would be to ask these 
would-be world-builders to work themselves for a 
while in unravelling a web of material conditions in 
the darkness of the unknown. If they work faith- 
fully I am sure that in distinguishing the ends of a 
few threads they will be rewarded for all their pains ; 
but I am equally confident that at the same time 
they will gain the conviction that hidden causes, as 
yet unsuspected, may intervene in the commonest 
phenomena of nature. Do not think I am a pessi- 
mist because I feel it my duty to emphasize these 
well-known facts. In the admirable work of Jevons, 
to which I have referred, you will find the same gen- 
eral doctrine still more emphatically stated and more 
fully illustrated. 



THE ATOMIC THEORY. 127 



LECTURE V. 

EXAMPLES OF SCIENTIFIC INVESTIGATION. 

IN the present lecture I shall ask your attention to 
two examples of scientific investigation, which 
will give a better idea than can any general dis- 
cussion, of the difficulties and uncertainties which 
perplex the student in almost every attempt to sub- 
stantiate the deductions from scientific generaliza- 
tions. I select the first example because it is within 
my own very recent experience; and although the 
history of science may present far more striking 
illustrations, I can speak of the perplexities incident 
to this investigation from personal knowledge; and 
as the results of the investigation have only recently 
been published,^ this fresh example may have the 
interest of novelty. 

The atomic theory is as old as Greek philosophy, 
and the best and most original exposition of the 
theory is still to be found in the famous heroic poem 
of Lucretius, ** De Rerum Natura," which appears to 
have been written about 58 B. C. The adaptation of 
the theory to explain the definite combining propor- 
tions of chemistry was made by John Dalton, of 

^ Published in Proceedings of the American Academy of 
Arts and Sciences, vol. xxiii. p. 119. 



128 prout's hypothesis. 

Manchester, in the early part of the present century, 
and since then these combining proportions have 
generally been called atomic weights. 

It was obvious from the first that of all tTie ele- 
mentary substances hydrogen gas must have the 
smallest atomic weight, and it was a natural inference 
that the atoms of all the elementary substances 
might be aggregates of this smallest indivisible unit. 

Such a theory was in harmony with the philosoph- 
ical conception that in the last analysis all materials 
could be reduced to the same ultimate essence, and 
that differences of qualities depended on the differ- 
ent affections of which this primordial material was 
susceptible. This theory was strongly advocated by 
Dr. Prout, an eminent physician in London, during 
the first half of this century, and the author of one 
of the well-known Bridgewater Treatises; and is 
known in science as " Prout's hypothesis." Obvi- 
ously, if this theory be true it would follow that all 
the atomic weights must be multiples of the atomic 
weight of hydrogen ; and if this last, as is usual, be 
taken as the unit of the system, the values of all 
other atomic weights must be expressed in whole 
numbers. Here, then, was an obvious deduction, 
which, if not substantiated by experiment must be 
fatal to Prout's hypothesis, an induction on trial. 

At the time when Prout wrote, the accepted values 
of many of the smaller weights were in accordance 
with his views; 'and the methods of chemical anal- 
ysis, by which the combining proportions of the 
elementary substances were determined, were not 
sufficiently accurate to distinguish, in the case of the 



DUMAS'S CONCEPTION. 1 29 

higher atomic weights, even the difference of a whole 
unit. As analytical methods were improved, marked 
discrepancies with the theory appeared; but so 
strong a hold had the conception taken on the minds 
of chemical students that these anomalies were over- 
looked or attributed to errors of observation; and 
for many years it was customary in works on chem- 
istry, to give as the values of the atomic weights the 
nearest whole numbers, instead of the actual mean 
of the observed values, and the practice Is still con- 
tinued in many works of accepted authority. 

At an early period in the discussion, a marked 
exception to the theory had appeared in one of 
the smaller and best known of the atomic weights. 
The combining proportion of chlorine, which forms 
with metallic silver one of the best defined chemical 
compounds, could be determined with great accu- 
racy; and all the experiments gave a value for its 
atomic weight closely approximating 35.5. This, 
and a few other similar facts, led the late Professor 
Dumas of Paris to entertain the idea that the atomic 
weights, if not all multiples of the whole hydrogen 
atom, might be multiples of the half or quarter atom ; 
or, in other words, that the hydrogen atom might 
itself be an aggregate of two or more smaller masses, 
which were the real units of the system ; and he was 
thus led to undertake the redetermination of a large 
number of the atomic weights, with the view of test- 
ing this modification of the original conception. His 
experiments were conducted with wonderful skill; 
and many of the new values he obtained for the 
atomic weights are still universally accepted by 



130 INVESTIGATION OF STAS. 

chemists. But the results had httle bearing on the 
question at issue; for it is obvious that by taking 
the unit small enough any result could be regarded 
as an even multiple of this unit within the limit of 
experimental errors. 

Soon after the publication of Dumas's paper, Profes- 
sor Stas of Brussels undertook a work of still greater 
magnitude. Stas had never been a believer in the 
hypothesis of Prout, and his aim was to push the 
analytical work to such a degree of refinement as to 
show conclusively that the results could not possibly 
be reconciled with any modification of that theory. 

Stas had been an associate of Dumas, and the lat- 
ter always spoke of his former assistant in terms of 
the highest admiration, declaring that he was the most 
accomplished experimentalist he had ever known. 
Thus Stas brought to the new investigation the 
highest skill, and, moreover, his position as the di- 
rector of the Belgian mint gave him command of 
means and appliances which enabled him to work 
on far larger quantities of material than any previous 
experimenter. As the error of an analytical process, 
other things being equal, is less in proportion to the 
quantity of material used, the advantage gained from 
the large scale of his experiments was very great. 
But at the same time these large amounts of material 
greatly increased the toil involved ; and the amount 
of labor which Stas devoted to this investigation was 
extremely great ; it can be appreciated only by 
those who are familiar with such processes. In this 
way however, Stas was able to reduce the merely 
accidental errors of the processes he employed within 



STRIKING FEATURE. I3I 

wonderfully narrow limits. He obtained values for 
several ' of the most fundamental atomic weights, 
which, though approaching whole numbers, still dif- 
fered from a multiple of the hydrogen unit by quan- 
tities far exceeding the probable error. At first 
these results were accepted as conclusive, and it 
seemed as if the hypothesis of Prout had been for- 
ever consigned to the tomb of unverified theories. 

Still, however, even from Stas's work the remark- 
able fact appeared that the atomic weights thus de- 
termined with so great labor and skill, though not 
exact multiples, approached very nearly to exact 
multiples of the atomic weight of hydrogen. If the 
several values were absolutely independent and dis- 
tributed by chance, the probabilities that they would 
all so nearly approach whole numbers was exceed- 
ingly small, and there was not one chance in ten 
thousand that such a distribution would occur as 
Stas's results exhibited ; so that on the whole Stas's 
work seemed to indicate that there might be some 
truth in the theory after all, if not in the exact form 
that had been supposed. 

This feature in the distribution of the atomic 
weights became still more marked as accurate values 
of the atomic weights of additional elements were 
obtained. Professor Mallet, of the University of Vir- 
ginia, was one of the first to call attention to the point 
just mentioned, in his admirable paper on the atomic 
weight of Aluminum, which his very accurate and 
accordant determinations had shown was very closely, 
if not exactly, a whole number ; and Professor F. W. 
Clarke, of Washington, in his work entitled " A Re- 



132 



ATOMIC WEIGHTS. 



calculation of the Atomic Weights," after summing 
up the results of a careful collation of all the trust- 
worthy determinations of these constants of nature, 
writes : " Enough has been said in this brief re- 
sume to show that none of the seeming exceptions 
to Front's law are inexplicable. Some of them in- 
deed, carefully investigated, support it strongly. In 
short, admitting half-multiples as legitimate, it is 
more probable that the few apparent exceptions are 
due to undetected constant errors than that the great 
number of close agreements, should be merely acci- 
dental. I began this recalculation of the atomic 
weights with a strong prejudice against Front's hy- 
pothesis, but the facts as they came before me have 
forced me to give it a very respectful consideration." 
The following table from the writer's work on " Chem- 
ical Fhilosophy," will make clear the point we are 



discussing: — 








ATOMIC WEIGHTS, MOST 


ACCURATELY DETERMINED. 


Hydrogen 


1.002 


Chlorine 


35.46 


Lithium 


7.01 


Potassium 


39-14 


Carbon 


12.00 


Calcium 


40.00 


Nitrogen 


14.04 


Bromine 


79-94 


Oxygen 


16.00 


Silver 


107.93 


Aluminum 


27.02 


Antimony 


120.00 


Sodium 


23-05 


Iodine 


126.85 


Magnesium 


24.00 


Barium 


137-14 


Phosphorus 


31-05 


Thallium 


204. 1 1 


Sulphur 


32.07 


Lead 


206.91 



This table includes all the values of atomic weights 
which up to 1882 could be regarded as known to 
within i-iooo of their value; and with one or two 
notable exceptions, there is no instance in which the 



DISTRIBUTION OF VALUES. 1 33 

value differs from a whole number by a quantity- 
greater" than the possible error, though not always 
the "probable error" of the processes employed in 
their determination. 

Were these numbers wholly independent of each 
other and distributed by no law, we should expect to 
find every possible intermediate value ; and the fact 
that they so nearly approach whole numbers cannot 
fail to produce on the mind the impression that there 
is some influence which tends to bring about this 
result. It may be that the discrepancies are due to 
such unknown constant errors as we have already 
described, and which, as every experimentalist knows, 
are always greatly to be feared. Or it may be that 
there is in nature a tendency to whole multiples, 
which in many cases is not fully reached. This last 
view, to be sure, is not compatible with our present 
conceptions of the atomic theory; but nature is not 
bound by this theory, nor should be our philosophy. 

The force of the evidence which such a distribution 
of values as the above table presents was brought 
home to the writer in his investigation on the atomic 
weight of antimony referred to in the previous 
lecture. After eliminating various causes of error, 
he was enabled to determine with great accuracy 
the atomic weights of antimony, silver, and bromine, 
in one and the same series of experiments, and it 
appeared that this ratio was — 

120.00: 108.00:80.00, 
with a probable error of less than one in the last 
decimal place. Here, then, is a ratio of whole num- 
bers, within the i-ioo of a single unit; and although 



134 REMARKABLE RATIO. 

the result may be no more impressive to others than 
many of the facts exhibited by the table, yet to 
the experimentalist who after long continued labor 
reaches such a result as this, the impression is in- 
evitable that there must be something more than 
mere chance in such coincidences. 

Since the ratio of the atomic weights of silver and 
oxygen have been determined with great accuracy, 
we can extend the above proportion to a fourth 
term, the atomic weight of oxygen, which appears 
also as a whole number, with a somewhat larger 
probable error. Still we have not reached the unit 
of the system, and when we attempt to extend the 
ratio to the atomic weight of hydrogen, we find 
that the most probable value from all experiments 
hitherto made gives the ratio, not of 1 6 to i, but of 
1 6 to 1.0025. 

If now we wished to refer to the hydrogen unit 
the atomic weights of antimony, silver, bromine, and 
oxygen, whose ratios of whole numbers had been 
determined as above, it was only necessary to divide 
all the terms of the above proportion by 1.0025, when 
we obtain the series of values given below the others, 
and all semblance of conformity to the hypothesis 
of Prout disappears, although of course the second 
series of numbers bear the same ratios to each other 
as the first. 



Antimony. 


Silver. 


Bromine. 


Oxygen. 


Hydrogen. 


120.00 


108.00 


80.00 


16.00 


1.0025 


119.70 


107.73 


79.80 


15.96 


I. 



The numbers in the lower of the two proportions 
appear as incommensurable as Stas maintained that 



QUESTION SUGGESTED. 1 35 

they were; and the same is true of most of the 
atomic "weights when given, as is usual in recent 
text-books on chemistry, on the basis of the same 
hydrogen unit. 

When, as the result of my investigation in the 
atomic weight of antimony, there were presented to 
me the ratios of whole numbers, as shown in the 
first of the above proportions, with the single ex- 
ception of the atomic weight of hydrogen, the 
question was at once suggested. Is the ratio of the 
atomic weight of oxygen and hydrogen in fact that 
of 16: 1.0025, as the general average of all trust- 
worthy determinations hitherto made seemed to in- 
dicate; or was there a constant error lurking in 
these results, which caused the very slight variation 
from the ratio from 16 to I required by the theory? 
I must confess that as I looked at the proportion as 
drawn out above, the conviction pressed upon me 
that this variation from the theory must be apparent, 
and I determined to ferret out the hidden error if 
possible. 

The problem was easily stated, but as is usual in 
questioning Nature, her answer was not so easily in- 
terpreted, and it has required several years of work 
to reach a definite conclusion. The results were at 
first baffling, and it was not until grave experimental 
difficulties had been overcome that definite conclu- 
sions could be reached ; and these conclusions were 
quite different from what had been anticipated. It 
is because this investigation is a good example of 
the methods of science, and an illustration drawn 
from personal experience of the general subject we 



136 FORMER INVESTIGATIONS. 

are discussing, that I venture to ask your attention 
to some of its details. 

On studying the methods by which the ratios of 
the atomic weights of oxygen and hydrogen had 
been determined, it was evident that they could be 
divided into two classes : first, the direct methods of 
determining the ratio, in which the proportions of 
oxygen and hydrogen uniting to form water were 
actually weighed ; secondly, the confirmatory methods, 
to whose results small value could be assigned inde- 
pendently of the first. Disregarding the last, as yield- 
ing no conclusive evidence on the question at issue, 
it appeared that all the trustworthy determinations 
had been made by essentially the same chemical 
process. This process consists in burning an unde- 
termined amount of hydrogen by means of oxide of 
copper, and weighing the water which results, and 
further determining the amount of oxygen combined 
from the loss of weight of the oxide of copper. 

The chemical process is a very simple one. Oxide 
of copper is a compound solely of copper and 
oxygen, and when hydrogen gas is passed over the 
heated oxide it takes up the oxygen to form water, 
and the copper is left in the metallic state. 

By weighing the glass tube containing the oxide 
before and after the experiment, we can determine 
the weight of oxygen which has combined with the 
hydrogen ; and by collecting the water formed, in 
appropriate desiccators, which are also 'weighed be- 
fore and after the experiment, we can find the weight 
of this sole product of the process, with extreme 
accuracy. 



NECESSARY CONDITIONS. 1 37 

By subtracting now the weight of the oxygen 
found, from the weight of the water found, we have 
the weight of the hydrogen which has combined with 
the oxygen in the process ; and the proportion be- 
tween the weight of the oxygen and the weight of 
the hydrogen is one half of the atomic ratio we 
are seeking; because, according to our theories, one 
atom of oxygen combines with two atoms of hydro- 
gen to form one molecule of water. 

The proportion by weight in which hydrogen com- 
bines with oxygen to form water is about that of I 
to 8. The atomic ratio about that of i to 16. 

Considering now the observed ratio of i to 8, it can 
be seen that the highest accuracy demands that each 
term of the proportion should be determined to an 
equal degree of exactness. Thus, if in a given ex- 
periment we have 8 grams of oxygen uniting with 
I gram of hydrogen, it is of no avail to weigh the 
oxygen to a tenth of a milligram, unless we can 
weigh the hydrogen to the same proportionate de- 
gree of accuracy; for an error 9-10 of a milligram in 
the weight of the water, or of 8-10 of a milligram in 
the weight of the oxygen, will have no more influence 
on the resulting ratio we are seeking than an error of 
i-io of a milligram in the weight of the hydrogen. 
Remembering now that i-io of a milligram is about 
the extreme limit of accuracy of our best balances, 
when loaded with more than a few grams of material, 
it can easily be seen that there is an obvious source 
of error in the determination we have described. 

The weights actually observed are, first, that of the 
water formed, and secondly, that of the oxygen used. 



138 SOURCE OF ERROR. 

The weight of the water can be determined to within 
a few tenths of a miUigram; that is, with all the 
accuracy with which our problem requires that the 
larger term of the proportion 8 to i should be 
known; and for the moment this weight may be 
regarded as established. 

It is quite different with the weight of the oxygen ; 
this last is found by weighing the glass tube contain- 
ing oxide of copper, before and after the experiment, 
and between the two weighings the tube is heated to 
a low red heat for several hours, while a stream of 
hydrogen gas is passing through it; and there are 
several causes which might lead to a slight variation 
in these weights, independently of the loss of oxygen, 
which has been used up in the process. It is un- 
necessary to discuss here what these causes are, but 
their effect would be unimportant if they only led 
to a small error in the observed weight of the oxygen. 
Unfortunately, this is not the case ; for when, in order 
to find the weight of the hydrogen, we subtract from 
the weight of the water, accurately known, the weight 
of the oxygen — which may be for the causes referred 
to, slightly erroneous — the whole error appears in 
the weight of the hydrogen thus found, and in the 
opposite direction. If, for example, the weight of 
the oxygen is too large, the weight of the hydrogen 
will be too small by exactly the same amount; and 
although the error may be an inconsiderable part of 
the weight of the oxygen, it may be a very appre- 
ciable quantity in the weight of the hydrogen. 

On the other hand, if a means could be devised for 
weighing the hydrogen, leaving the oxygen to be 



DUMAS'S REMARKS. 139 

determined by subtracting this smaller weight from 
the weight of the water, then a small error in the 
observed weight of the hydrogen would have no 
appreciable effect on the weight of the oxygen. 

Professor Dumas, who made by far the most ex- 
tended series of observations by the old method, 
fully recognized the source of error to which I have 
referred, and in his paper on the subject wrote as 
follows : — • 

" Of all analyses which a chemist can undertake, 
that of water is the one which offers the greatest un- 
certainty. In fact, one part of hydrogen unites with 
eight parts of oxygen to form water; and nothing 
would be more exact than the analysis of water, if 
we could weigh the hydrogen as well as the water 
which results from its combustion. 

*'But the experiment Is not possible under this 
form. We are obliged to weigh the water formed 
and the oxygen used to produce it, and to calculate 
the weight of the hydrogen consumed in the process 
from the difference of these two weights. Thus an 
error of 1-900 in the weight of the water, or of 1-800 
in the weight of the oxygen, affects the weight of the 
hydrogen by a quantity equal to 1-90 or 1-80 of its 
value. As these errors are in the same direction 
they are added to each other, and we shall have an 
error amounting to 1-40." 

On entering upon the investigation it was evident 
from the outset that no advantage was to be gained 
by multiplying determinations by the old methods. 
The work had repeatedly been done by the best 
masters of the science, with all the accuracy of which 



140 WEIGHING A GAS. 

the method was capable. The only hope of improve- 
ment lay in finding some method of weighing the 
hydrogen with sufficient accuracy ; and it was essen- 
tial to determine this weight to within i-io,ooo, or 
at least 1-5000 of its value. 

A gas can only be weighed by enclosing it in a 
glass globe or some similar receiver, and hydrogen 
is so exceedingly light that its total weight can only 
be a very small fraction of the containing vessel; 
moreover, as the buoyancy of the air is fourteen and 
one half times as great as the weight of the hydrogen, 
the variations in buoyancy caused by changes in at- 
mospheric conditions have an all-important effect in 
the apparent weight. The late Professor Regnault, 
of Paris, devised a very ingenious method of com- 
pensation which could readily be applied in this case. 
It consisted in balancing the globe containing the 
hydrogen, hung to one arm of the balance, by a sec- 
ond globe of exactly the same volume and made of 
the same material, hung to the opposite arm, and so 
arranging the balance-case that both globes should 
hang in the same enclosure and therefore be equally 
affected by atmospheric changes. This method I 
applied in the problem before us, and after a number 
of trials I found it possible to make the compensation 
so accurate that the weight of my globe holding 
five litres of gas did not vary more than i-io of a 
milligram through large changes of temperature and 
pressure. In order now to weigh the hydrogen with 
this degree of accuracy, it was only necessary to ex- 
haust the air from the glass receiver, and after bal- 
ancing it as described, to fill it with hydrogen, when 



METHOD OF BURNING. I41 

the increased weight (only about 4-10 of a gram 
with my" apparatus) was the weight of the hydrogen 
required. 

In order to burn this hydrogen I used essentially 
the same apparatus as previous experimenters, pas- 
sing the gas over heated oxide of copper, collecting 
the water formed, and determining its weight. Every 
detail of the apparatus was the result of careful con- 
sideration, and in many cases was only reached after 
numerous experiments. 

There were many difficulties to be overcome, but 
the result left nothing to be desired, and thus far the 
method was as perfect as the conditions required. 

Everything now turned upon introducing into our 
globe absolutely pure hydrogen, and here the great- 
est difficulties were met. 

Fortunately at this point I secured for my work 
the assistance of a young chemist, Mr. T. W. Rich- 
ards, my former pupil and present assistant, of whose 
experimental skill I can speak as warmly as did Du- 
mas of Stas. 

A part of the difficulties of filling the globe with 
pure hydrogen were wholly mechanical, and the only 
ones which it is important I should mention here are 
the difficulties we met in procuring absolutely pure 
gas. 

It will be obvious that an exceedingly small amount 
of impurity would be fatal to the accuracy of my 
method. If the hydrogen we introduced into our 
globe carried with it only 1-10,000 part of its volume 
of atmospheric air, — an impurity which it is exceed- 
ingly difficult to avoid, on account of the rapid dif- 



142 EFFECT OF SLIGHT IMPURITY. 

fusion of hydrogen and the pervasiveness of our 
atmosphere, — this impurity would increase the appar- 
ent weight of the hydrogen by i-io of a per cent, and 
cause an error that would be fatal to the degree of 
accuracy we were seeking. 

In our earlier determinations we drew the hydrogen 
gas from a large self-acting generator charged with 
sulphuric acid and zinc. We used in the generator 
pure, but not the purest materials, which it would 
not have been practicable to procure on the scale on 
which we then expected to work ; and we trusted to 
a complicated system of purifiers to remove the 
traces of sulphurous oxide or other chance impuri- 
ties which the gas might contain. With hydrogen 
thus prepared and purified, we made a large number 
of determinations. We give only a few of these in 
the table below, but those here exhibited are a fair 
soecimen of the whole. In each case the numbers 
express the atomic weight of oxygen referred to 
hydrogen as unity ; and it will be noticed that these 
values are not only far below the average of the 
previous results, 15.96, but also that they differ 
widely from each other. 

PRELIMINARY RESULTS. 

15-793 15850 15.835 

15.790 15.937 15.820 

It was now obvious that the varying values must 
result from impurities in the hydrogen, and as we 
knew that our purifiers did their work efficiently, we 
were persuaded that the impurity must be the nitro- 
gen of the atmosphere which entered our apparatus 



FIRST SERIES OF RESULTS. I43 



by diffusion at its many joints. We sought to stop 
such leaks by every means possible, and we thus suc- 
ceeded in obtaining better and better results, but 
there was still far too great irregularity to make the 
determinations of any value, and we were finally 
forced to reduce the scale of our experiments. 

We then constructed an apparatus in which hydro- 
gen was prepared on a smaller scale from chemically 
pure zinc and hydrochloric acid. The extent of the 
purifiers was greatly reduced; and the number of 
joints reduced to only two or three, and these were 
all carefully sealed with impervious cement. With 
this apparatus we made the first five determinations 
given in the table on page 148. In this table we 
give, in the first column, the weight of the hydrogen 
burnt; in the second column, the weight of water 
obtained ; in the third column, the atomic weight of 
oxygen deduced from these weights after making 
allowance for the buoyancy of the air; and in the 
last column, the difference between each atomic 
weight and the average of the five- 
It will be seen that we had now reached a very 
different result. All the values are closely concord- 
ant, the maximum difference from the average cor- 
responding to less than l-io of a milligram of the 
hydrogen weighed; and also this mean value very 
closely agrees with 15.96, the average deduced from 
previous results. 

Indeed, the agreement was as close as we could 
possibly expect. If there was an error it could not 
arise from any fluctuating cause, like the diffusion of 
air which we had previously encountered; it must 



144 SECOND AND THIRD SERIES OF RESULTS. 

be some constant error depending on the process. 
Moreover, we felt equally sure that the error, if any, 
could not arise from our method of weighing the 
hydrogen, for our result was essentially the same as 
that obtained by the older process, in which the oxy- 
gen, and not the hydrogen, was weighed. Still, to 
trace out any error, if existing, we next sought to 
vary the process of preparing the hydrogen, and con- 
structed an apparatus with equal care in which hydro- 
gen was evolved by electrolysis, that is, by the action 
of a current of electricity on a mixture of water and 
hydrochloric acid. With the gas procured from the 
new apparatus, we made five additional determina- 
tions, which follow the first five in the table just re- 
ferred to. By inspecting the column of differences, 
it will be seen that the concordance in this second 
set is even greater than in the first. Apparently, then, 
we had reached a maximum which we could not 
exceed by varying the process ; but that there might 
be no question on this point, we set up an apparatus 
still simpler than the last two, by which hydrogen 
gas was prepared from the metal aluminum, and a 
solution of caustic potash ; and with hydrogen thus 
obtained, we made still five other determinations, 
whose results are given below in the same table. 
Here again, the average given is essentially identical 
with the averages of the other two series. 

The evidence now seemed to be conclusive; the 
average of these fifteen experiments must be the true 
value of the atomic weight of oxygen, within a very 
small limit of probable error. The process had been 
varied in every conceivable way, and with the same 



CONSTANT ERROR DISCOVERED. T45 

identical result. Nevertheless, these results were 
affected by an important constant error, which, al- 
though so obvious when pointed out, had been over- 
looked in spite of all our care. The publication 
above referred to was already in print when our 
attention was called to the point by Lord Rayleigh, 
who had been working on a similar problem. 

In adopting the method of Regnault for weighing 
the hydrogen gas subsequently burnt, we had as- 
sumed with this eminent physicist that the volume 
of the globe remained invariable after the air had 
been exhausted, when of course the pressure of the 
air on the exterior surface was no longer balanced 
by the tension of the gas within. As Regnault had 
himself experimented on the compressibility of glass, 
and as the least change in the volume of the ten 
litre globe which he used must have most seriously 
affected the values he obtained for the densities of 
the aeriform substances on which he experimented, 
— namely, air, oxygen, nitrogen, hydrogen, and car- 
bonic acid, values which have since been regarded as 
among the most accurate constants of science, — it 
seemed safe to assume with him that the effect of the 
atmospheric pressure on the globe when exhausted 
was insensible. And it should be remembered that 
the investigator must always build on previous work, 
and that there could be no progress if he felt obliged 
to verify all the data which he necessarily employs. 
He must accept data which are regarded as well- 
established, and in selecting these data he is neces- 
sarily guided by authority. There could be no 
better authority than Regnault on the point in ques- 



146 AFFECTS PREVIOUS RESULTS. 

tion ; his results have been hitherto accepted without 
question, and a vast amount of experimental work 
has been based upon them. 

Nevertheless, the globe which Regnault used in 
his determinations of gas densities, when exhausted, 
must have been sensibly compressed by the atmos- 
pheric pressure ; and must, therefore, have appeared 
to weigh more than when full of gas, in consequence 
of the diminished displacement, and hence the less- 
ened buoyancy of the atmosphere. This increase of 
weight must have been about 1.29 milligrams for 
every cubic centimeter by which the volume of the 
globe was compressed ; and the observed weights 
of this globe-full of the different gases on which 
Regnault experimented must, therefore, have been 
too small by the same quantity. 

Unless the globe which Regnault used has been 
preserved it is not now possible to correct his re- 
sults ; since the amount of compression of a glass 
vessel under a constant pressure depends on condi- 
tions which vary widely and must be separately 
determined for each vessel. Fortunately, in our 
work the same glass globe had been used from the 
first, and there was no difficulty in determining the 
exact amount by which our results had been influ- 
enced by the effect under discussion. For this pur- 
pose it was only necessary to weigh the globe under 
water, first when exhausted, and afterwards when 
full of air. Under these circumstances, if there was 
any change of volume, the difference of buoyancy 
would become very marked, and could be accurately 
estimated. 



CORRECTION FOUND. I47 

A description of the details of these additional 
experiments would be out of place here. It is suffi- 
cient to say that the shrinkage of the glass balloon 
we used, when exhausted, amounted to nearly two 
cubic centimeters, or about 0.0004 of its exterior 
volume; that in each of our determinations the true 
weight of the hydrogen gas burnt was nearly two 
milligrams greater than the apparent weight; and 
that after making correction for this altered weight 
the atomic weight of oxygen deduced from our ex- 
periments is 15.869, instead of 15.953 as before given. 

After such a catalogue of difficulties encountered, 
and errors avoided, it may well be asked, How can 
we be sure that there may not be still other causes 
of constant error invalidating our results? Obvi- 
ously we cannot be sure. All we can do is to work 
earnestly and conscientiously for the truth, and leave 
the future to revise our results and correct our mis- 
takes. In this way the truth will be finally reached, 
although the progress may be slow and halting, and 
our individual labor may appear to have' been lost. 

But although the exact value of the atomic weight 
of oxygen may hereafter be found to differ more or 
less from the number we have finally reached, the 
general result of our work has been to invalidate 
the hypothesis of Prout. This theory appears to 
fail at the most critical juncture. Is there then no 
significance in the analogies we have pointed out? 
Has the close approximation of the ratios of so 
many of the atomic weights to a proportion between 
whole numbers no meaning? I feel persuaded that 
there is a significance in the analogies, and a mean- 



148 TABLE OF RESULTS. 

ing in the coincidences ; but it is not a significance 
or meaning that we can as yet interpret, and we must 
be content to wait for more knowledge and larger 
views. 

ATOMIC WEIGHT OF OXYGEN. 

First Series. 

Weight of Hydrogen. Weight of Water. Atomic Weight of Oxygen. 
0.4233 3.8048 15.977 

0.4136 3-7094 15-937 

0.4213 3.7834 15.960 

0.4163 z-ii\^ 15-941 

0.4I3I 3.7085 15.954 







15.954 _[_ 00048 




Second Series. 




0.4II2 


36930 


15.962 


0.4089 


3.6709 


15-955 


0.4261 


3-8253 


15-955 


04197 


3-7651 


15.942 


0.4144 


3-7197 
Third Series. 


15-953 

15 953 i 0.0022 


0.42205 


3-7865 


15-943 


0.4284 


3.8436 


15.944 


0.4205 


3.7776 


15.967 


0.43205 


3.8748 


15-937 


0.4153 


3.7281 


15.954 


0.4167 


3-7435 


15-967 



15.952 ± 0.0035 

Total Average 15-953 ± 0.0017'. 

After correcting for shrinkage of balloon under the atmos- 
pheric pressure, — 

Final result . . . 15.869 i 0.0017. 



DEDUCTIONS FROM THE LAW OF GRAVITATION. 1 49 

The history of physical astronomy since the publi- 
cation of the '' Principia " furnishes abundant illustra- 
tions of the various features of scientific deduction on 
which we have dwelt in this lecture. There has been 
a continuous development of the deductions from the 
law of gravitation, and in this work the mathematical 
genius of two centuries has found abundant employ- 
ment. The law of gravitation is one of the few 
fundamental principles of nature of which we feel 
confident that we have found the exact expression. 
Most of the laws of physical science are only laws of 
approximation ; that is, laws with which the phe- 
nomena of nature closely agree, but which exhibit 
certain discrepancies that lead us to believe that with 
larger knowledge we may reach more accurate repre- 
sentations of the truth. But the law of gravitation 
appears to be exact, and we have every reason to 
believe that in the progress of science it will remain 
essentially unaltered. It is, moreover, a very simple 
relation. In consequence of the mode of action 
which we call gravity, and which is as mysterious an 
agent now as when first recognized, a pull is exerted 
between any two masses of matter in the universe, or 
the parts of any two masses, which is proportional 
directly to the products of the two masses, and in- 
directly to the square of their distance apart, — as 
may be expressed by the very simple algebraic 
formula : 

Unlike any other physical forces with which we are 
familiar, this attraction is not influenced by the na- 



150 PROBLEM OF THE THREE BODIES. 

ture of the material of the masses, by the nature of 
the medium interposed, by the proximity of other 
masses, or by any other conditions, except solely the 
quantity of material in the masses and the distance 
between them. Newton himself made these points 
the subject of an experimental investigation, and his 
results have been confirmed by other astronomers, 
who, like Gauss, have been ready enough to question 
the finality of the law ; and it is only after repeated 
doubts have been resolved in its favor that we have 
settled into the belief that it is precisely correct. 
Still, simple as the law is, to trace its action between 
the heavenly bodies becomes at once a problem of 
great dif^culty. 

So long as astronomers limited themselves to the 
question of central forces and considered only the 
action of the sun on the individual planets, the prob- 
lem was comparatively simple, and admitted of the ele- 
gant solution which Newton gave in the " Principia ; " 
but when the universality of gravity came to be recog- 
nized, and it became a question of the mutual action 
and reaction of all the bodies in the universe, not only 
of the sun on the planets but of all the planets on each 
other, the problem assumed a complication with which 
no human power could grapple, and whose complete 
solution was impossible. But setting aside for the 
time the more general problem in which many of the 
forces acting were so slight that they could be over- 
looked, there was in the fore-front of astronomy the 
case of the moon, acted on strongly by both the 
earth and the sun; and thus arose the famous prob- 
lem of the three bodies, which alone has exhausted 



PLANETARY PERTURBATIONS. 151 

the powers of the mathematicians from Newton's 
time to our own. When only three bodies simultan- 
eously attract each other the compHcation of effects 
is so great that only approximate calculations are 
possible, and the complete solution of this compara- 
tively simple astronomical problem has yet to be 
given, Newton himself grappled with this subject, 
and so far succeeded as to give a tolerably accurate 
representation of the moon's motions ; and the only 
open bitterness shown during his life appears to have 
been displayed towards his contemporary Flamstead, 
the first Astronomer Royal, who showed unwilling- 
ness to furnish him with the observations he needed 
to compare with his theory. 

The consideration of the mutual attractions of the 
planets and the sun brings us to the more complex 
problem of planetary perturbations. The complete 
solution of this problem even in its simplest form is 
hopeless, and the principle on which the calculation 
of planetary perturbations proceeds is to reject every 
effect which does not lead to a quantity appreciable 
in observation. The quantities thus rejected are 
indefinitely more numerous and complex than the 
few larger terms which are retained ; and in combin- 
ing these last, numerous assumptions have to be 
made in order to simplify the problem. The solution 
reached therefore is merely partial, and the results 
approximate; but by such tentative methods great 
perfection has been reached in the theory of the 
planetary orbits. 

One of the greatest triumphs of astronomical de- 
duction, and yet one of the most striking illustrations 
II 



152 PERTURBATIONS OF URANUS. 

of the incompleteness of its methods, was the dis- 
covery of the planet Neptune. For many years the 
observations of the planet Uranus, discovered by the 
elder Herschel in 1781, had differed markedly from 
the theory of its orbit, even after making every allow- 
ance for the perturbations caused by its nearest 
associates, Saturn and Jupiter; and what was more 
note-worthy, the error had gone on increasing rapidly 
from year to year. That this effect might be due to 
the disturbing influence of an unknown outer mem- 
ber of the solar system was a reasonable supposi- 
tion; and if so, the theory of astronomy ought to 
be able to predict the elements of the orbit, and, 
therefore, to point out at any moment the position of 
the disturbing body. Here, however, as in other 
problems involving the mutual action of several 
bodies, a complete solution was impossible, and the 
tentative methods of calculation were long and te- 
dious; so that astronomers were slow to undertake 
the work. But in 1843 the investigation was be- 
gun by Adams at Cambridge, England, and also, at 
about the same time, by Leverrier at Paris, and the 
issue is well known. 

Leverrier communicated his result to the astrono- 
mer Galle, by a letter received at Berlin September 
23, 1846; and the same evening the planet was 
found, nearly in the place pointed out By a for- 
tunate coincidence, a map of that portion of the 
heavens — one of the sheets of Bremiker's Berlin star 
map, then recently published — facilitated the search; 
and Galle quickly found a star of the eighth magni- 
tude, not on the map, which the observations of the 



DISCOVERY OF NEPTUNE. 1 53 

next two days showed must be the object sought. 
A year previously, however, Adams had communi- 
cated to Professor ChalHs of the Cambridge Observa- 
tory, the results of his independent calculation, which 
subsequently proved to correspond closely with those 
of Leverrier; but although search had been made, 
and, as afterwards appeared, the planet had been 
seen, it had not been recognized from want of such 
a map as the Berlin astronomer possessed. 

Thus two separate mathematicians, without concert 
with each other, reached the same solution of this 
difficult problem, and their prediction appeared to be 
precisely verified. Could there be a more striking 
confirmation of theory, a greater achievement of 
human intellect? And yet in its greatest triumph 
mathematical analysis displayed its weakness. 

On March 16, 1847, within six months of the dis- 
covery of the new planet. Professor Benjamin Peirce 
stated to the American Academy of Arts and Sci- 
ences, in words which I quote from their Proceed- 
ings, "The planet Neptune is not the planet to 
which geometrical analysis has directed the tele- 
scope." This declaration, first received with distrust, 
proved to be fully justified. The planet of the theory 
had a mean distance from the sun of from 35 to 37.9 
times that of the earth, with a corresponding period 
of revolution of from 207 to 233 years. The actual 
Neptune has a mean distance of only 30, with a 
period of about 168 years. At the time of the dis- 
covery, the planet of the theory and the actual 
Neptune had approximately the same apparent posi- 
tion, or, as astronomers say, were in conjunction. 



154 HAPPY ACCIDENT. 

But this was a *' happy accident," and to this chance 
the discovery of the actual planet must be ascribed. 

As Professor Peirce clearly showed at the time, 
this singular result depended on the approximate 
and tentative character of the method of calculation 
necessarily employed. Had the conditions been ex- 
actly known, and had the mathematical analysis been 
exhaustive, the actual planet which caused the per- 
turbations would doubtless have been at once pointed 
out; but several approximate solutions of the prob- 
lem were possible. Of these the theoretical planet 
was one, the actual planet was a second, and still 
others might be distinguished. 

The problem could not be approached without 
making an assumption in regard to the solar dis- 
tance, and as both mathematicians were led, by the 
so-called law of Bode, to make the same assumption, 
they came to the same approximate result. Unfortu- 
nately, the law assumed to regulate the relative dis- 
tances of the planets from the sun conspicuously 
failed in the case of Neptune, and we have heard but 
little of it since. According to this law, the solar 
distance of Neptune should have been about 39.6 
times the earth's distance. Leverrier tried successive 
assumptions, beginning with 39.1, and finding that 
with a diminishing value the conditions of the prob- 
lem were at first better satisfied, while afterwards the 
discrepancies increased, he concluded that the value 
must be within the limits stated above. Adams 
followed in part the same course, although his cal- 
culations were less full. The planet found had a 
distance of 30 only, and if the calculations had been 



METHOD OF CALCULATION. 1 55 

extended to this limit, another solution of the prob- 
lem would have appeared which proved to be the 
true one. But the second solution was not suspected; 
because at an assumed distance of 35.3 there was a 
singular point which introduced peculiar disturbances. 
In a word, the theoretical planet was an approximate 
solution of the problem for the field of research cov- 
ered by the analysis ; while the real planet was out- 
side of this field, and separated from it by a barrier 
which the partial analysis could not overstep. 

You cannot find in the whole history of science a 
more striking illustration than this, both of the power 
and of the limitations of deductive thought. The dis- 
covery of a new planet appeals strongly to the imagi- 
nation of men ; and the story of the mathematician 
who from his study directed the astronomer where to 
find a predicted member of the solar system, is con- 
stantly told as an evidence of intellectual power, — less 
frequently as a signal instance of mental limitations 
and human fallibility; and yet the last is the more 
impressive lesson. Here, however, as so often in 
human affairs, weakness was made strength. Through 
striving, the planet was discovered and the boundaries 
of knowledge were extended. 

Obviously there was a large element of chance, or 
— as I prefer to call it — Providence, in the discovery 
of Neptune ; and such chances have been repeatedly 
the turning-points in the history of science. The 
accidental breaking of a crystal of Iceland spar re- 
vealed to Hawy the structure of crystalline bodies. 
A chance reflection of light from the windows of the 
Luxembourg Palace in Paris disclosed to Malus the 



156 RESULTS OF CHANCE. 

laws of polarization. The twitching of the legs of a 
frog first made known to Galvani the existence of low 
tension electricity. The swing of a compass-needle 
on his lecture-table opened to Oersted the phenomena 
of electro-magnetism, and was the simple beginning 
from which have come all the wonderful applications 
of electrical currents. In the remark that Lagrange 
is said to have made of Newton, that " such accidents 
happen only to those who deserve them," there is a 
deeper philosophy than was probably intended. It 
must be remembered that to a higher intelligence 
there can be no such thing as accident; and that 
" the fortuitous concourse of atoms," like any other 
event, would be seen to have its antecedents and 
causes if our imperfect perceptions could take cog- 
nizance of their existence. Moreover, even on our 
plane, numbers would fail to convey a conception of 
the utter hopelessness of the chance, on the doctrine 
of probabilities, that the right accident would happen 
to the right man at the right time. 

On the other hand, such experience as I have 
narrated should show us that close coincidences of 
approximate results are in themselves no sure test of 
truthfulness, and carry with them but little weight. 
Men of science are familiar with this principle, and 
almost every investigator could enforce it by numer- 
ous examples. But on most men such coincidences 
make an extraordinary impression ; and many of the 
delusions of society, including the astrology of the 
past and the pseudo-spiritualism of the present, find 
their chief support in the apparent coincidences which 
a wide latitude of variation permits. 



COINCIDENCES OFTEN ILLUSORY. 1 5/ 

Lastly, such experience should teach us how unsafe 
it is to rely implicitly on popular statements of scien- 
tific deductions. An impression widely prevails that 
however important a knowledge of the general results 
of science may be, it is not necessary that the literary 
man or the general scholar should acquaint himself 
with scientific methods. But it is obvious, from what 
has been said, tnat no accurate knowledge of the facts 
of nature is possible without a knowledge of the 
methods by which the facts have been established. 
The phenomena of nature are so complex, and the 
simplest effects so modified by concurring agencies, 
that they cannot be fully comprehended unless 
studied in their natural relations. The phenomena 
described in text-books are often not realities of 
nature, but ideal relations which are as much abstrac- 
tions as the conceptions of geometry. As systems 
of science such books have their value; but their 
necessarily general statements are not often a sound 
basis for theological arguments. We cannot safely 
reason from the facts of nature until we know them 
with all their limitations ; and if I have enabled you 
to realize this truth, my chief object in this lecture 
has been gained. 



158 INDUCTION AND DEDUCTION CONTRASTED. 



LECTURE VI. 

LAWS OF NATURE. 

TN the previous lectures we have endeavored to 
-*- make clear the distinction between induction and 
deduction in scientific investigation. Induction is the 
discernment, recognition, and verification of a general 
principle of nature previously unknown. The dis- 
cernment may be more or less accurate, the recogni- 
tion more or less satisfactory, the verification more 
or less complete ; but the process is essentially an 
intuitive act of the mind working upon previous 
knowledge or experience, and familiar acquaintance 
with natural phenomena. Hence, under favorable 
conditions, it is more or less spontaneous, and cannot 
be regulated by methods or directed by rules. It is, 
in a word, the product of genius. 

Deduction is the evolution by logical processes, 
mathematical or otherwise, of the consequences, in- 
ferences, or implications which a general principle 
includes or suggests. It may be more or less direct, 
more or less difficult, more or less exhaustive ; but in 
any case the results were implicitly involved in the 
premises established or assumed. It is a creature of 
methods, a slave to rules, and deals with syllogisms, 
equations, observations, experiments, and measure- 



OPINION OF JEVONS. 1 59 

ments of every kind. It is the task of the many, the 
work of the great army of scientific laborers. 

Induction raises the level of human knowledge; 
deduction expands that knowledge. Induction opens 
new fields of investigation ; deduction explores these 
fields. Induction discloses hidden treasures ; deduc- 
tion appropriates and uses them. Induction soars; 
deduction creeps. Induction aspires ; deduction con- 
templates. Induction is imaginative; deduction is 
reahstic. Induction is theoretical ; deduction is prac- 
tical. Induction is bold and confident; deduction is 
cautious and sceptical. 

I am well aware that the position I have taken 
is not wholly in harmony with the mechanical view 
of induction which the authority of Bacon has so 
strongly impressed on English thought; but I still 
feel confident that I am in sympathy with the great 
body of scholars who are practically familiar with 
scientific methods. 

Professor Jevons, who as a logician classified in- 
duction as inverse deduction, thus wrote in regard to 
the nature of the process itself: "All induction is 
but the inverse apphcation of deduction ; and it is by 
the inexplicable mental action of a gifted mind that a 
multitude of heterogeneous facts are caused to range 
themselves in luminous order as the results of some 
uniformly acting law." This is the best authority I 
could quote ; and I now pass on to consider certain 
distinctions among the results of induction, which 
I hope will serve to make our conceptions of the 
subject still clearer. 

Of all the results of induction there are none so 



l60 LAWS OF NATURE DEFINED. 

familiar or so striking as the laws of nature ; and of 
the aspects of the material universe there is none 
which is more appalling to the religious mind than 
the reign of law. Law and Providence seem incom- 
patible and mutually exclusive. "The wind bloweth 
where it listeth," without regard to the tempest-tossed 
ship freighted with the hopes of nations. The laws 
of motion do not spare precious lives when a broken 
rail turns the rushing train from its appointed track. 
The law of gravitation made no discrimination among 
the victims on whom the Tower of Siloam fell ; and 
so fire and flood, pestilence and famine, tornado and 
earthquake, have ever involved the good and the bad 
alike in common ruin. 

Law is inexorable, cruel, pitiless ; and no wonder 
that as thus viewed the conception of law should be 
a hindrance to faith. But this view of nature is a 
misconception which arises from a superficial knowl- 
edge of the facts ; and the law of the text-books, or 
of the popular imagination, is for the most part an 
ideal phantom. Correct views on this subject are of 
such supreme importance in natural theology that I 
propose to devote two lectures to a discussion of some 
of the distinctive features and manifold variations 
which the so-called laws of nature present. 

A law of nature is simply a declaration or state- 
ment of a certain order, sequencey or relation, observed 
among material phenomena. Jevons says, " The laws 
of nature are simply general propositions concerning 
the correlation of properties which have been found 
to hold true of bodies hitherto observed." And 
again : " A law of nature is not a uniformity which 



LAWS OF NATURE NOT EFFICIENT CAUSES. l6l 

must be obeyed by all objects; but merely a uni- 
formity ^hich is, as a matter of fact, obeyed by those 
objects which have come beneath our observation." 
Thus the first law of motion declares that any mass 
of matter continues in its state of rest or motion until 
acted on by some force external to itself. The law 
of Mariotte affirms that the volume of a given mass 
of gas is inversely proportional to its tension. The 
law of gravitation states that any two masses of matter 
attract each other with a force directly proportional 
to the product of the two masses, and inversely pro- 
portional to the square of the distance between them ; 
and so \<'e might multiply examples. Notice, noth- 
ing is affirmed in regard to the mode of action in 
either case. The phenomena observed may be the effect 
of a single cause ^ or the resultant of several causes ; 
but the law takes no cognizance of any such feature. 
It only recognizes the order, sequence, or relations 
it describes. This is a most important point, to which 
I would ask your special attention. 

The laws of nature are simply statements of ob- 
served relations. They are not efficient causes or 
modes of action of any kind ; and whatever features 
with such an aspect may be superimposed upon the 
formal propositions in the description or by the im- 
agination, is something superadded to their only real 
sanction as laws of nature. 

There may seem to be in the statement of the law 
of gravitation, as usually given and as enunciated 
above, something conflicting with the positive position 
here laid down. When it is said that one mass of 
matter attracts another, or, as Newton himself enun- 



1 62 "HYPOTHESES NON FINGO." 

elated the law, every particle of matter in the universe 
attracts every other particle, it might appear as if a 
mode of action was declared in the proposition ; and 
I have no doubt that the law is so understood by 
nine out of ten of the students who repeat the state- 
ment. But Newton intended to convey no such con- 
ception ; and no such conception was received by the 
scholars for whom he wrote. 

It is true, however, that one mode of explaining 
the law is to assume that there resides in the ulti- 
mate particles of matter some unknown virtue which 
determines the attraction. But this is a pure hypo- 
thesis, one of those redundancies referred to above, 
for which the law must not be held accountable. 
When Newton himself was asked whether he had any 
conception of this kind he is said to have replied: 
" Hypotheses non fingo." 

Moreover, the whole tendency of modern science is 
entirely opposed to any theory which assumes an 
inherent potency in the particles of matter ; and, in 
the case of gravitation, such an hypothesis, as we 
shall see in the next lecture, is beset with insuperable 
difficulties and objections. It would be better if we 
could enunciate the law without using the word ** at- 
tract; " but this cannot be done without an awkward 
circumlocution. Of course what is meant is simply 
that two bodies, if free to move, would act as if they 
were pulled by a force varying according to the well- 
known law; and what is true of this proposition is 
equally true of the statement of every recognized law 
of nature. All such propositions are intended to 
declare solely a relation between phenomena ; and in 



DANGER OF MISAPPREHENSION. 1 63 

any case if the language implies more, there is some- 
thing accessory, which careful criticism will distin- 
guish and eliminate. 

When such propositions are briefly enunciated in 
ordinary language there is always danger of misap- 
prehension and confusion; and hence one of the 
objections to unguarded popular statements of scien- 
tific principles to which I have referred. For instance, 
from the ordinary statement of the law of inertia — 
every mass of matter continues in its state of rest or 
motion until acted on by some force — I know by 
experience that a large majority of students derive 
the idea that an original state of motion must have 
been the effect of some force; and yet this is pre- 
cisely the reverse of the impression that the words 
were intended to convey; and in general I may say 
that it is rare that students acquire from text-books 
on physics correct conceptions of the fundamental 
principles of mechanics. 

The popular conception which so constantly asso- 
ciates causation with a law of nature undoubtedly 
arises from the figurative use of the word law in this 
connection. Law in human relations implies a law- 
giver; and therefore we associate with human laws 
the personal attributes of the law-giver. The laws of 
the Medes and Persians were inflexible ; the laws of 
the Romans were equitable ; the old laws of England 
were cruel; the modern EngHsh laws are more mer- 
ciful, — simply because, each and all, they reflected 
the character of the men who made and administered 
them ; but to call the law of gravitation pitiless is 
like calling the multiplication table inexorable, or a 



1 64 EVIL AND LAW. 



prisoner's chains cruel. Of course it will be said such 
language is figurative ; but the difficulty is that the 
distinction between the figurative and the real is not 
always kept clear ; and this is not the only case in 
which mental confusion and logical fallacy have 
arisen from the use of familiar terms. 

Still, while all must admit that the definition of a 
law of nature as here given is conformable to the 
best usage among scientific scholars, it may be said, 
the awful fact remains that amidst the misfortunes of 
man, the whole aspect of external nature is hard and 
pitiless, and fine-drawn distinctions do not relieve 
the suffering that the relentless march of natural 
phenomena entails. Certainly not ! We cannot solve 
the terrible problem which the evil of the world 
everywhere presents. This is a fact of nature, as well 
as law. But do not confound it with law. Its sources 
are far deeper, among those hidden springs of being 
whence flow also the equally mysterious relations of 
personality and free will. Do not then by any per- 
version of thought associate malevolence with the 
laws of nature. To a finite being, law means reliance, 
confidence, and repose. It is heaven-born, beneficent 
order; but it has no potency in itself, and may be 
used by the powers of evil as well as by the powers 
of good. 

Another popular misconception of the relations of 
a law of nature appears in the trite argument so often 
urged as a disproof of the Christian miracles. It is 
impossible to conceive, it is said, that a law of nature 
should be broken. Certainly it is, and so it is im- 
possible to conceive that the qualities of metallic 



CONSTANCY OF LAW. 1 65 

gold should be changed. Were the properties of 
gold changed in the least degree the material would 
be no longer gold ; and so, were the relations predi- 
cated by the law of gravitation altered, we should at 
once have a different law. I do not say that either 
of these changes is possible, much less probable; but 
I do maintain that they are both conceivable, and 
not so inconsistent with our actual knowledge of the 
order of nature as to render the supposition inhe- 
rently absurd. So far from this, the transmutation of 
the metals was the favorite problem of the elder 
chemists ; and it is well known that Sir Isaac New- 
ton, whose scientific sobriety cannot be questioned, 
devoted a great deal of time to experiments in this 
direction; and, although in a somewhat different 
form, the question has been reopened in our own 
day. So also, as before said, the most eminent men 
of science have seriously considered whether the 
law of gravitation might not be modified under new 
conditions. 

Could each law be traced to a single definite cause, 
it is obvious that a change in the law would imply a 
corresponding change in the cause, and, therefore an 
alteration of purpose, or method, inconsistent with 
our philosophy either of an intelligent first cause or 
even of a self-evolving, self-sustained cosmogony. 
But these are not the conditions. The laws of nature 
are relations of phenomena which, in most cases, at 
least, are obviously resultants of many causes whose 
action is inextricably commingled ; and it is perfectly 
possible to conceive of a new element introduced 
into one of the chains of causation which would 



l66 CONSTANCY OF LAW. 

utterly alter the final result. I do not say that this is 
possible ; but I do say that we have no positive knowl- 
edge which makes such a contingency impossible. 

Man cannot increase by the smallest fraction either 
the material or the energy he employs ; but he can 
introduce conditions into the chain of causation, by 
which he is able to control and determine events, and 
even to alter the face of the earth. Why, then, may 
not new issues appear in nature? Why may not 
a new force overrule an old one? Why indeed may 
not unrecognized agencies, which have always existed, 
and whose effects have been slowly accumulating, at 
any moment appear as important factors in human 
affairs and relations? Not only do I see no reason 
for believing that we possess an exhaustive knowl- 
edge of nature's powers ; but on the contrary I am 
persuaded that even in the most familiar fields, there 
may at any time appear indications of forces hitherto 
undiscovered, which may be capable of momentous 
effects. Remember that it is only a century ago 
that the first indications were noticed of a power 
which is now one of the chief agencies of our civiliza- 
tion. And what were these indications? Only the 
momentary twitching of a frog's legs ! 

Let it be understood that I make no claim to sub- 
stantiate or explain miracles ; but I do maintain that 
we cannot disprove Divine interference in the course 
of nature ; and that the scientific probabilities against 
such occurrences may be fairly set off against the 
moral presumptions in their favor. To me it seems 
to be a question of evidence, upon which our knowl- 
edge of the laws of nature has no bearing. More- 



*' SPIRITUAL MANIFESTATIONS." 167 

over, to my mind the marvellous in these events is no 
weighty evidence against their credibility. What could 
be more marvellous than many of the revelations of 
modern science? As I distinctly remember, the re- 
volving of the vanes of Crooke's radiometer, seemed 
to me, when I first saw the instrument, as much out 
of the ordinary course of nature, as would the turning 
of water into wine. Investigation showed that the 
motion was the normal result of a force which had 
always been acting, though unsuspected ; and so at 
any moment a strange phenomenon may put us in 
possession of a new force which will overrule all the 
powers of the world, and make more than the dreams 
of Aladdin sober realities. Nothing is too marvellous 
to be believed, provided it is substantiated by satis- 
factory evidence. 

Why, then, it may be asked, do you not believe in 
mind-reading, clairvoyance, faith-cure, and other so- 
called spiritual manifestations, with which the popu- 
lar mind is from time to time deluded? Simply 
because they are not attested by satisfactory evidence. 
It is upon this ground, and not on account of their 
strangeness or improbability, that we hesitate to ac- 
cept them. There are doubtless facts, and very in- 
credible facts, concerning these matters, that are well 
attested ; and there may be agencies which have 
never been recognized. But the phenomena claimed 
to exist are so complex, and so obscured by uncon- 
scious self-deception, or by actual imposture, that no 
undoubted truth, or definite relation, has as yet been 
established. 

Societies have been formed, both in this country 
12 



1 68 GLOOMY ASPECT OF NATURE. 

and in England, for the promotion of psychical re- 
search; but it may be questioned if, in the presence 
of so many problems of nature which are within our 
grasp, it is good policy to expend energy on those 
which, for the time at least, are hopelessly involved ; 
and also whether it is wise to concentrate public at- 
tention on abnormal states, or diseased conditions of 
mind, which will certainly be excited and spread 
thereby. Nevertheless, if a single clearly new phe- 
nomenon were elicited by such investigations, who 
can question that it would be studied with the same 
zest as was Crooke's radiometer? 

Of course I do not forget the paralyzing impression 
of desolation and despair which in some moods the 
uniformity of nature forces on the mind; but this 
impression, though an unquestionable feature of hu- 
man experience from the earliest times, has no per- 
tinency to the laws of nature. This aspect of nature 
affects most strongly minds of an imaginative temper- 
ament, and is one which the study of science rather 
tends to soften and elucidate. It is seen as clearly 
by the poet as by the philosopher ; and it inspires 
fatalism more often than scepticism. It is a part of 
the discipline of life, to which all sorts and conditions 
of men must bow. This aspect of nature has, then, 
no special relations to our scientific knowledge ; only 
the facts of science are often perverted to sustain the 
terribly gloomy philosophy it suggests. Moreover, 
science has pointed out the one consideration which 
may solve the mystery. 

The insect's life is often only a summer's day 
whose sunshine knows no change ; and may not the 



babbage's calculating engine. 169 

uniformity of nature during human life be like a 
shifting scene to Him with whom we have to do? 
Such a doctrine is wholly consistent with our knowl- 
edge of the laws of nature ; and the point has been 
so forcibly put by the late Charles Babbage, in the 
" Ninth Bridgewater Treatise," the most profound of 
those celebrated works, that I cannot do better than 
to quote his words. After describing the calculating 
machine, which is so inseparably associated with his 
name, and showing that such an engine might work 
invariably by one law of action, during any finite 
number of steps however great, and yet at a prede- 
termined point introduce a break in the series, — for 
instance, after counting up the natural* number to a 
term expressed by a hundred miUion digits, — he 
writes : " If every letter now before the reader's eye 
were changed into a figure, and if all the figures con- 
tained in a thousand such volumes were arranged 
in order, the whole together would yet fall far 
short of the vast induction the observer would have 
had in favor of the truth of the law of natural num- 
bers ; yet shall the engine, true to the prediction of 
its director, after the lapse of myriads of ages, fulfil 
its task and give that one, the first and only excep- 
tion, to that time-sanctioned law." What would 
have been the chances in favor of the perfect contin- 
uity of the series immediately prior to this break? 
Certainly, we may add, as great as are the chances 
that the sun will rise to-morrow. 

Now this same machine, as Mr. Babbage also 
showed, may be so constructed and set as to change 
its law after an appointed number of terms, and then 



I/O BABBAGE'S CALCULATING ENGINE. 

proceed to follow a new law as invariably as before. 
Thus, after giving the natural numbers for a certain 
period, it might suddenly begin to give square or 
cube numbers; and it is possible to conceive of a 
machine by which such transitions might be indefi- 
nitely repeated. 

If such things are possible in human mechanism, 
why not in the scheme of nature? That in the 
short history of science we have not observed such 
changes is no proof that they may not take place. 
If they do come to pass we should expect from all 
analogies that they would come with extreme slow- 
ness, according to our measures of time, and without 
observation. And certainly during the geological 
ages changes have come to pass for which we can 
give otherwise no clear account. 

Of course such considerations as Babbage has 
so eloquently urged are no arguments, but they do 
help the imagination ; and this is a question in which 
the imagination has raised all the difficulty, and is 
therefore chiefly to be addressed. 

We have tacitly assumed thus far that the laws of 
nature are all equally definite and equally exact ; but 
this is very far from being true. In most cases, at 
least, the phenom.ena correlated under a law admit 
of a more or less wide variation ; and the proposi- 
tion which we call a law is an ideal rather than an 
actual relation, — an abstraction, rather than an entity. 
This is the next point to which I wish to ask your 
attention ; and its bearing on the previous consider- 
ations is obvious. For if it shall appear that the laws 
of nature vary with different relations, and are not 



DEFINITE LAWS. 171 



the hard and fast rules which have been assumed; 
that they are modes of thought, and not modes of 
action ; then all that has been said in regard to the 
independence of causation, and the possibility of 
interference, will be seen to have still greater force 
than at first appeared. 

Very few of the recognized laws of nature are ab- 
solutely definite ; and of these few, with the exception 
possibly of the law of gravitation, the invariability 
must be assumed ; for it cannot be proved, at least 
absolutely. In the present state of knowledge we 
should class as among these definite laws, the law of 
conservation of mass, the law of conservation of 
energy, the laws of motion, and the law of gravita- 
tion. Now, although we may have no question that 
all these laws are absolutely fixed, and can never be 
expected in the least degree to alter in their mani- 
festation, yet there is not one of them which is sus- 
ceptible of experimental proof, except, to a limited 
extent, the law of gravitation. 

Take, for example, the first law of motion, the law 
of inertia, as it is also called, and which we have 
before more than once enunciated. We cannot 
demonstrate experimentally that a body will con- 
tinue in a state of motion until acted on by some 
external force. On the surface of the earth, even 
under the most favorable conditions, all motion is 
soon arrested by friction, or by some other mode of 
impact ; and the most we can do is to show that in 
proportion as such resistances are removed, the 
longer the motion continues, — a form of inference 
which has been called " the principle of successive 



1/2 LAW OF INERTIA. 

approach," but which is obviously no proof. Could 
the law of inertia be verified experimentally, perpet- 
ual motion would be possible; but even with all 
our experimental skill we have not made the most 
distant approach to such a condition. 

It is a mistake of ignorance to infer that perpetual 
motion means unlimited work ; and yet it is this very 
erroneous inference which alone gives a popular in- 
terest to the question. Work done by a moving 
body necessarily involves loss of motion; and the 
effects of friction are merely examples of this general 
principle. Perpetual motion is theoretically possible, 
but work without the loss of motion, or the expendi- 
ture of energy in some form, is inconceivable; and 
the assumption impHes a confusion of mechanical 
conceptions. It is unnecessary for our purpose to 
dwell on this point, and we allude to it only because 
it serves indirectly to illustrate the character of the 
law under consideration. Nor need we do more than 
refer to the grand displays of perpetual motion re- 
vealed to us by astronomy, which seem at first sight 
to be most conspicuous illustrations of the principle. 
But the law is here so overlaid and obscured that 
observations on the motions of the planets cannot 
be regarded as a direct proof of its validity. Indeed, 
originally the law was an assumption made to ex- 
plain these very motions, and is, therefore, an induc- 
tion based on astronomical facts, not a deduction 
that can be demonstrated by them. 

As with the law of inertia so is it with the law of 
conservation of mass. We cannot demonstrate that 
the amount of material in nature has never been 



CONSERVATION OF MASS. 1 73 

increased by the smallest amount. All we can do 
in any case is to show that the amount of material 
with which we experiment is not perceptibly altered 
in the various transformations through which it 
passes, — assuming of course that the amount of ma- 
terial, or to use a technical term, the mass, is accu- 
rately measured by the weight. In a chemical 
process, when we can weigh all the materials con- 
cerned, we find that within the unavoidable experi- 
mental errors, often very large, the sum of the 
weights of the products of the process is exactly 
equal to the sum of the weights of the factors; and 
after a very wide experience with similar results we 
assume that the two sums are always exactly equal. 
Hence we represent every chemical process as an 
equation, writing on the left of the sign of equality 
the several symbols which represent the weights of 
the factors, and on the right the corresponding sym- 
bols which represent the weights of the products. 
Obviously, however, we can never demonstrate the 
exactness and universality of the law which our 
chemical equations assume. The constancy of the 
law is of necessity a question of inference. Still, as 
in the case of inertia, we can appeal to phenomena 
which render the inference in the highest degree 
conclusive. 

There are, for example, a very large number of 
chemical processes which it is possible to conduct 
m an hermetically closed vessel, — as in a sealed pre- 
serve jar; so that by weighing the vessel before 
and after the experiment, it can be shown that no 
change of weight has come from the chemical pro- 



174 CONSERVATION OF MASS. 

cess which has taken place inside, — a result which 
we should confidently expect, since nothing could 
get in or out of the sealed vessel. 

The burning of charcoal in oxygen gas, under 
such conditions as just described, furnishes a very 
striking illustration of the principle under discussion. 
When a lump of charcoal burns, a sohd material, 
the fuel, is converted into an aeriform substance, 
the smoke ; and the result seems at first sight glar- 
ingly to contradict the assumed law; but when we 
burn the coal in a closed jar it is obvious that as 
there has been no change of weight, there can have 
been no loss of material; and it is further evident 
that the substance of the coal must have been ab- 
sorbed by the oxygen gas to form the aeriform 
product we call smoke. 

We can now pass to the earth as a whole ; and re- 
garding our dwelling-place as a globe isolated in space 
from which no material escapes, and into which hone 
enters, — except an occasional meteorite, — we can at 
once recognize relations similar to those of a sealed 
jar, in which all terrestrial nature appears as a grand 
illustration of the conservation of mass. But obvi- 
ously such illustrations, although they may be the 
basis of well-founded inferences, are no proofs of the 
absolute exactness and invariability of the law ; and 
a study of either of the other laws we have classed 
as exact would bring out the same features. But 
this is a subsidiary point, and it is not necessary to 
dwell upon it further. 

The laws classed as exact present also another 
character worthy of your consideration, which, al- 



FUNDAMENTAL CONDITIONS. 1 75 

though it cannot be definitely formulated in the 
present state of our knowledge, is probably funda- 
mental ; and it distinguishes these special cases from 
the great body of the laws of nature whose relations 
we shall study later. Such principles as the laws of 
motion, and the laws of conservation, whether of 
mass or of energy, seem to be fundamental relations 
of the material universe ; and not the modes of ac- 
tion of external agencies. They are like the essen- 
tial qualities of matter, — extension, impenetrability, 
mobility, — and not like the accidental qualities, which 
may be regarded as superimposed upon matter by 
the action of some mode of energy, — such as color, 
temperature, or magnetism. Consequently they are 
simple instead of complex relations. 

Consider, for instance, inertia, which is often classed 
as a quality of matter. This is not an active but 
wholly a passive relation, as the common use of the 
word " inert " indicates. Matter has no powder within 
itself to change its state or condition in any way. 
Such changes in all cases imply an external agent, 
and an expenditure of energy, which is to be distin- 
guished from the passive mass on which it acts. 

It has been said that the original atoms contained 
the potency of all possible being; and if by this is 
meant that they were the beginnings of things, — 

^' . . . rudis indigestaque moles, 
Nee quicquam nisi pondus iners, congestaque eadem 
Non bene junctarum discordia semina rerum, — " 

the proposition is harmless enough, if we accept the 
general theory that atoms are the final result of the 



176 POTENTIALITY OF ATOMS. 

analysis of matter ; but if it is meant that the atoms 
have actual creative potency, and all future being 
involved in their substance, in the same sense that 
the flower is infolded in the bud, then it is a suffi- 
cient answer to all such speculations to say that 
they are wholly at variance with the manifest ten- 
dency of modern science. If there be one thing 
more marked in that tendency than another, it is to 
distinguish energy and matter as two distinct and 
separate entities ; and to regard matter as wholly 
inert, utterly lifeless and dead, except in so far as it 
is controlled and energized from without. We be- 
lieve this to be the correct view, not only in regard 
to such manifestations of material bodies as we refer 
to heat, light, and electricity ; but also in regard to 
those seemingly inherent forces which hold the parts 
of a body together, and determine the effects of 
cohesion, elasticity, and the like. 

For example, we distinguish among the conditions 
of magnetic phenomena what we call the " field of 
force." Masses of iron brought into that field — that 
is, into any space thus conditioned — become at once 
magnetic, and attract or repel each other as the case 
may be. Now it is a plausible conception that we 
live in a space conditioned not only by magnetism, 
but by various other agencies, which may determine 
the cohesion and structure of solid bodies. Every 
year I show to my class an experiment which I 
never witness myself without being strongly im- 
pressed by the wonderful relations which it illus- 
trates, and the still more wonderful relations it 
suggests. On the top of a board, resting on the 



FIELD OF FORCE. 1 77 



poles of a powerful electro-magnet, I place a large, 
loose pile of wrought-iron nails. When the current 
of a dynamo-machine passes through the coil of the 
instrument, a magnetic field is established through- 
out all the space in the neighborhood of the poles ; 
and with this the board in no way interferes, al- 
though it keeps the nails from direct contact with 
the magnet itself. As soon as the current passes, 
and the field is established, the loose nails, by their • 
mutual attractions, — thus determined, — become a 
tough, plastic mass, which can be moulded into the 
form of an arch, or of any similar structure. But 
when the current is broken the magnetic virtue of 
the field disappears, and the structure that had been 
reared, crumbles into nails. Analogy suggests that 
the atoms of matter, inert in themselves, are simi- 
larly conditioned, and that all structures would be 
resolved, and all forms of matter disappear, if the 
Presence which sustains them were withdrawn. 

Now, just as the first law of motion appears to be 
merely a declaration of a passive quality of matter, 
so it seems to me all the other laws we have classed 
as exact are fundamental attributes either of matter 
or of energy. This may not appear as the laws are 
usually stated ; but an analysis of the relations thus 
enunciated will always show their true character. 
Thus in regard to the law of conservation of mass, 
to which we have just referred in another connection, 
— it would be easy so to state the law as to make it 
appear arbitrary and anomalous. That in every 
chemical change the sum of the weights of the prod- 
ucts formed should be exactly equal to the weights 



178 CONSERVATION OF MASS. 

of the factors consumed ; for example, that when 
water is resolved by an electrical current into oxygen 
and hydrogen, the combined weights of these two 
aeriform substances should be exactly equal to the 
weight of the liquid water used up in the process ; 
or, what is still more remarkable, that when coal or 
wood burn, the weight of the smoke added to the 
weight of the ashes will be, to the smallest fraction of 
a grain, exactly equal to the weight of the fuel which 
has disappeared, and for the most part flown up the 
chimney, — all this does seem at first sight to be such 
a precise conformity to weights and measures as 
could never have been secured unless specially or- 
dained ; but a few moments' consideration will show 
that this law, so far from being an ordinance super- 
imposed as it were upon matter, is a relation neces- 
sarily arising from its very constitution. In any 
mechanical process you at once recognize that there 
can be no real loss of material. When silver and 
gold bullion are coined or made into ware and trink- 
ets, you confidently expect, from your knowledge of 
material relations, to find all the metal in the manu- 
factured articles, — of course excepting a small loss 
from dispersion by attrition, abrasure, or otherwise, 
for which you can readily account. Why should not 
the same be true in a chemical process? If there be 
no loss of precious metal when one hundred pounds 
of silver are coined at the mint, why should there be 
any loss when the same amount of bullion is con- 
verted into nitrate of silver by the manufacturing 
chemist? Certainly, not only can we find no "suffi- 
cient reason " for expecting a change of relations 



LAW OF COMBINING PROPORTIONS. 1/9 

under such circumstances, but also the more we 
study material relations the more evident does it 
appear that conservation of mass is simply the mani- 
festation of the persistency of the mode of being we 
call matter. In other words, the study of the rela- 
tions of matter, and even our own familiar experience, 
has produced the conviction that beneath the eva- 
nescent qualities of changing substances and the de- 
caying forms of organic structures, there is a material 
substratum which is permanent and unchangeable; 
and that the law of chemistry we have been studying 
is simply the manifestation of this fundamental es- 
sence of matter. The illusion which is produced by 
the escape of colorless aeriform matter in the burning 
of fuel, and in many other less familiar chemical pro- 
cesses, is easily corrected by conducting the ex- 
periment in an air-tight vessel, as we have before 
described. 

The same essential feature appears in the second 
of the great laws of chemistry, which we have already 
described as the law of combining proportions. 
That hydrogen gas should combine with oxygen gas 
to form water in the exact proportions of 2.000 to 
15.869, as was shown in the last lecture, does seem 
at first sight as accidental or arbitrary a relation as 
could well be imposed on these elementary sub- 
stances; but if we look at the subject from another 
point of view, it will be seen that some definiteness of 
relation is implied by the other essential attributes of 
matter, even though our present knowledge may not 
enable us to see the reason of the precise value of 
the proportion in a given case. It is obvious, for 



l80 LAW OF COMBINING PROPORTIONS. 

example, that assuming the supply of oxygen unlim- 
ited, we should expect to obtain twice as much water 
by burning twice as much hydrogen ; and so, on the 
other hand, were the supply of hydrogen unlimited, 
we should expect the same result by using twice as 
much oxygen; otherwise all our knowledge of ma- 
terial relations would be confounded. But this implies 
that the relative weights of hydrogen, oxygen, and 
water, which concur in the famiHar process of burning 
hydrogen gas, must be definite, — although we have 
no means of predicting that the definite proportion 
should be exactly that of 2.000 to 15.869 to 17.869. 

Take, as another example, the simple chemical pro- 
cess which results when we bring together carbonate 
of soda, hydrochloric acid, and water. The products 
of this process are common salt, carbonic acid gas, 
and a small additional amount of water. Here again 
common-sense, as we might say, tells us that we must 
proportion our carbonate of soda to the amount of 
carbonic acid gas we desire to make. If we need 
three times as much gas we must take three times as 
much soda, and so in regard to any of the other 
materials concerned in the process ; but this implies 
a definite relation between the several factors and 
products of the chemical change, or, in other words, 
this familiar experience and common-sense imply 
the law of definite proportions. 

In the two cases last cited these so-called laws of 
chemistry are evidently, as we have before said, 
merely fundamental relations of matter, and not the 
modes of action of external agents. To the same 
category belongs the law of conservation of energy, 



LAW OF GRAVITATION. l8l 

and so obviously that I need not press the point ; but 
in regard to the great law of gravitation there is a 
manifest difficulty of interpreting the phenomena 
from this point of view. As we have already pointed 
out, the usual statement of the law implies an 
attractive force, and therefore an active power of 
great potency. Nevertheless, I am inclined to the 
opinion that here also the facts are best explained 
on the view that gravitation is simply a manifesta- 
tion of a fundamental relation between energy and 
mass. 

There are several circumstances which would sup- 
port the opinion thus expressed, although I have 
only time to allude to them here. In the first place, 
gravity is the only attractive force which is directly 
proportional to the mass. Magnetic and electrical 
attractions follow wholly different and far more com- 
plex laws. In the second place, the diminution of 
gravity with the square of the distance is simply the 
law of the diffusion of any radiant energy through 
space ; as may be seen in the intensity of illumination 
on screens at different distances from a luminous 
source. In the third place, the attraction of one 
mass is not in the least influenced by the proximity 
of similarly attracting masses. Thus, each of two 
weights on a scale-pan exerts its specific effect inde- 
pendent of its association; but two magnets or two 
electrified bodies when placed in juxtaposition do 
not exert the same invariable concurrent action. In 
the fourth place, the attraction of gravity is wholly 
independent of the intervening medium. Two bodies 
on the opposites sides of this globe would attract 



1 82 LAW OF GRAVITATION. 

each other with the same force whether the earth 
were in the way or not ; while electrical or magnetic 
attraction is very greatly influenced by the nature of 
the dielectric or diamagnetic which intervenes. In 
fine, activities which are superinduced, like electrical 
or magnetic attractions, follow wholly different and 
vastly more complex laws than the simple relations 
to mass and space which gravity exhibits. Hence 
the grounds of the opinion expressed above that the 
law of gravitation is a proposition which expresses, 
not the mode of action of a special force or agency, 
but simply a fundamental and necessary relation 
between energy and mass. 

I freely admit that the opinion I have expressed 
in regard to the laws classed as exact may be open 
to philosophical objections, and I do not advance it 
as a well-grounded, much less as an accepted doc- 
trine. Since, however, I expect to show in my next 
lecture that the great body of natural laws, as enun- 
ciated in our systems of science, are merely ideal 
relations, which the phenomena of nature approach, 
but which are rarely if ever realized, I felt it incum- 
bent on me to give a clear account of those funda- 
mental principles that appear to be more exact. 
My one object is to make clear to you the aspect 
of the laws of nature as seen from the standpoint 
of a student of physical science, with all the in- 
definiteness which the view presents, and with the 
impenetrable clouds which limit the prospect on 
every side. Do not, however, accept my opinions, 
or rely on my judgment; but study the phenomena 
for yourselves, not as drawn in sharp outlines by popu- 



CAUTION REQUIRED. 183 

lar writers, but as exhibited by nature, with all their 
limitations, all their variations, and all their obscurity. 
Make sure of the actual facts ; so that you shall build 
your philosophy on a firm and enduring basis that 
cannot be moved. 



13 



1 84 LAW OF MARIOTTE. 



LECTURE VII. 

DETERMINATE AND INDETERMINATE LAWS. 

OF the great body of the laws of physical science 
which are described in the treatises on physics 
or chemistry, I could not select a fairer illustration 
than the law of Mariotte. This law was discovered 
during the last half of the seventeenth century, wholly 
independently, by the Abbe Mariotte in France and 
by the famous English philosopher Boyle, and is 
often called by English writers " the law of Boyle." 
Since that time all the relations of the law have been 
repeatedly and carefully investigated, and there are 
few principles of science in regard to which our 
knowledge is more precise. According to the usual 
formula this law declares that the volume of a given 
mass of gas is ittversely as the pressure to which it 
is exposed ; or in other words, that as the pressure 
increases or diminishes, the volume contracts or ex- 
pands in precisely the same proportion. For exam- 
ple, if we have a perfectly flexible balloon, partially 
inflated, the volume of the confined gas will contract 
or expand in absolutely the same proportion as the 
pressure of the air on the outside is increased or 
diminished. We can also enunciate the law in another 



CONCOMITANT CONDITIONS. 1 85 

form, which applies to any mass of aeriform matter, 
whether confined or not, — saying that the density of 
a given atmosphere is directly proportional to its 
tension. But since the tension of a gas must neces- 
sarily balance the pressure to which it is exposed, 
and since the density of a gas must increase as its 
volume diminishes, the last statement only describes 
another phase of the same principle. 

This law discovered by Mariotte is of fundamental 
importance in many departments of chemistry and 
physics, especially in meteorology; but in nature its 
simple working rarely if ever appears. The volume 
and density of a mass of aeriform matter not only 
varies with the external pressure or internal tension, 
but similar and as great changes are caused by varia- 
tions of temperature. Considerable although less 
marked effects are produced by moisture, and in pass- 
ing from one place to another a sensible change may 
be caused by the variations in the intensity of gravity. 
In any case the observed phenomenon is the resultant 
of all these partial effects, which may either concur or 
tend to balance each other. Constantly, then, in 
practice, the law must be disguised and its action 
obscured. The same is true of all similar laws. The 
phenomena of nature are usually very complex results, 
and such laws as the one we are discussing are the 
simpler elements into which we attempt to analyze 
the phenomena. But this, although a perplexing, is 
only an incidental circumstance, and we must con- 
sider the aberrations of the law itself. 

Even when abstracted from all concomitant condi- 
tions, so far is the law of Mariotte from exact that it 



1 86 DEVIATIONS FROM THE LAW. 

holds absolutely in no single instance, unless inferen- 
tially as a passing phase of a continuous change. 
When we study the subject minutely and pay regard 
to small differences we find that each distinct aeriform 
substance has a rate of its own, and is, as it were, a 
law unto itself. At the common temperature most 
gases, as nitrous oxide, carbonic acid, ammonia, 
oxygen, nitrogen, and the mixture of the last two we 
call air, contract under pressure to a perceptibly 
greater extent than the law authorizes. At high 
pressures the deviation becomes very marked, and as 
we approach the pressures under which the gases 
are condensed to liquids no semblance of the law is 
left. Hydrogen, on the other hand, the lightest con- 
dition of aeriform matter, alone contracts less than the 
law requires. Hydrogen therefore seems to present 
unique relations, and to stand apart by itself. But 
the experiments of Regnault indicate that this rela- 
tion depends to a large extent on temperature. He 
observed that although carbonic acid deviates widely 
from the law of Mariotte at the freezing-point of 
water, it conforms almost precisely to it at the boiling- 
point So also he noticed that air deviates from the 
law much less at an elevated temperature than at the 
ordinary temperature of the atmosphere ; and he con- 
cluded that a temperature could easily be attained at 
which the deviation would become insensible to our 
means of observation. He even thought it probable 
that at a very high temperature the air would again 
deviate from the law, but in the opposite direction, like 
hydrogen at the ordinary temperature. Generalizing 
these observations it is supposed that the same would 



HISTORY OF THE LAW. 1 87 

be true of all gases, — namely, that with each aeriform 
substance there is some temperature at which it con- 
forms to Mariotte's law ; that at all temperatures below 
this point the gas is compressed more than the law 
authorizes, and at all temperatures above this point it 
is compressed less than the law demands. In a word, 
the law is an ideal relation, which is realized, if at all, 
only under the concurrence of conditions which it is 
impossible to command. 

Mariotte's law illustrates in a very forcible manner 
the character of the large class of the so-called laws 
of nature we are considering, and its history furnishes 
one of the best examples of refined scientific investi- 
gation. I could readily multiply examples, but further 
discussion would be tedious, and would add nothing 
to the force of my argument; for I feel confident 
that it will be generally allowed that I have selected 
as fair and as typical an illustration as I could find. 
In my work on " Chemical Physics " I have given at 
some length the history of the law of Mariotte, and I 
would refer you to that book for the details ; feeling 
confident that while they fully bear out the impres- 
sion I have endeavored to give here in a few words, 
a careful study of the particulars will give you a much 
larger comprehension of the subject I am seeking to 
illustrate. In bare outline the history can be briefly 
told. 

The compressibility of gases was in the first place 
studied with a comparatively rude apparatus, and a 
simple law was discovered, which was accepted as 
the absolute truth. Later, when the methods of 
investigation had become more accurate, it was 



1 88 THE GRAPHICAL METHOD 

found that the law was not general ; but it was still 
maintained in regard to air, until finally the refined 
experiments of Regnault proved that it failed here 
also. Still the law remains as an ideal truth toward 
which nature tends, but which is never fully reached, 
and we can even trace the action of the agents which 
produce the perturbations. So it is with most physi- 
cal laws. They are not realized with mathematical 
exactness, but are ideal truths always more or less 
false in each particular case. When we are able to 
go behind the phenomena to their proximate causes, 
we shall undoubtedly find that the law and its varia- 
tions are merely different phases of the workings of 
one complex system ; but it is doubtful whether by 
man's limited powers the anomahes of nature will 
ever be fully explained, or its discords resolved. 
More probably, as we go forward in our investiga- 
tions, and continually widen our generalizations, the 
last generalization of all will bring us into the pres- 
ence of that Intelligence of which all natural phe- 
nomena are the direct manifestation. 

When a physicist can discover no simple relations 
between conditions or phenomena obviously inter- 
dependent, his usual method of proceeding is to plot 
his observations on paper, on some system of co- 
ordinates, and draw a curve through the points, thus 
found. The process is a simple one, and with the 
aid of an example can easily be made intelligible, 
even to those who do not understand the technical 
terms with which the so-called graphical method is 
usually described. 

The solubility of a substance in water varies with 



OF REPRESENTING PHYSICAL RELATIONS. 1 89 

the temperature, usually increasing, but sometimes 
diminishing, as the temperature rises, and at rates 
which vary with different substances between wide 
limits. There is an obvious connection between the 
weight of a substance which will dissolve in one 
hundred parts of water and the temperature; but 
no definite law connecting these quantities can be 
discovered. Assume that we have determined ex- 
perimentally the weight in grams of some salt, for 
example, nitre (KNO3), that will dissolve in one 
hundred grams of water at various temperatures be- 
tween its freezing and boiling points, and that we 
have tabulated the results. Assume also that we have 
a sheet of what is called " co-ordinate" paper, divided 
off into little squares like a multiplication table, as 
in the accompanying figure. On the lower horizon- 
tal line, called the *' axis of abscissas," we mark off 
the temperature in degrees, and on the left-hand ver- 
tical line, called the "axis of ordinates," we mark the 
weight in grams. Taking now the data we have tab- 
ulated, and noticing that at 0° thirteen grams of nitre 
(KNO3) dissolve in one hundred parts of water, we 
follow up the vertical line marked o^, until we come 
to the horizontal line marked thirteen grams, and 
there fix the first point. Seeing next that at 15° 
one hundred grams of water dissolve twenty-five 
grams of nitre, we follow up the vertical line marked 
15° to the horizontal line marked twenty-five grams, 
and the intersection fixes a second point. As at 
30° one hundred grams of water dissolve forty-five 
grams of nitre, we find a third point by following up 
the vertical line marked 30° to the horizontal line 



190 THE GRAPHICAL METHOD 

marked forty-five grams ; and so we proceed with 
each of the experimental data we have found. Thus 
we obtain as many points as there are observations, 
and then with a free hand we draw a curve as nearly 
as possible through all the points. On the diagram 
we have given, a number of curves showing the vary- 
ing solubility of several chemical compounds in water 
have been thus drawn. Such curves represent to 




the eye what has been called the " law of the vari- 
ation," using however the word " law " in a still less 
definite sense than we have as yet employed it. 
They not only exhibit the general order of the phe- 
nomena, but they enable us to fix with close approx- 
imation values between the points at which the 
observations were made. Thus we see from the 
figure above that while the solubility both of potas- 
sium chloride (K CI) and of barium chloride (Ba CI2) 



OF REPRESENTING PHYSICAL RELATIONS. IQI 

increases slowly, but at a uniform rate with the tem- 
perature, the solubility of nitre (K N O3) varies very 
rapidly, and at a constantly increasing rate. Again, 
the solubility of sodium sulphate (Nag SO4) presents 
what is called a singular point, increasing rapidly 
up to 34° and then diminishing. Lastly, if we wish 
to determine the solubility at a given temperature 
of any of the salts here represented, we have only 
to follow up the vertical line corresponding to the 
temperature, until it intersects the curve of the 
substance in question. Then on following from 
the point of intersection the horizontal line to the 
left, we read off on the vertical axis, the number 
of grams of the substance which will dissolve in 
one hundred parts of water at that temperature. 
Other physical phenomena can be plotted and in- 
terpreted in a similar way. 

Every algebraic equation involving two variable 
quantities corresponds to some kind of plane curve ; 
and so, on the other hand, every plane curve may be 
represented symbolically by an algebraic equation 
of a more or less complex character, containing the 
unknown quantities. Thus, for example, the solu- 
bility of nitre graphically represented by the curve 
above described, may also be expressed by the 
equation — 

S:= 13.32-}- 0.5738/ -{-0.017168/2-j- 0.0000035977/3 

in which / stands for the temperature in degrees 
centigrade, and S for the number of grams of salt 
which at this temperature will dissolve in one hun- 
dred grams of water. In this expression the value 



192 ALGEBRAIC EXPRESSION. 

of one of the variables, the quantity sought, is given 
in the terms of the ascending powers of the other 
variable, in this case the temperature, — each term 
being multiplied by a numerical coefficient, whose 
values are deduced from experimental data. Equa- 
tions of this general form are the simplest, although 
not always the most concise, means by which such 
relations can be algebraically expressed. The sci- 
ence of mathematics, however, gives us the means of 
treating the subject exhaustively, so that after distrib- 
uting the errors, we can express our results in the 
most concise manner of which the observations admit, 
as well as in the form best adapted to computation. 
It furnishes us with methods and guides for interpola- 
ting, — that is, of calculating from numerical results of 
definite experiments, what would have been the value 
of intermediate results, — or even for assigning values 
beyond the limits of the experimental data, exterpo- 
lating, as Airy called it. But in its details this sub- 
ject cannot be understood without some knowledge 
of mathematics ; and further discussion would be out 
of place in these lectures. It is only with the broader 
relations of the subject that we are here concerned ; 
and it is obvious that such algebraic expressions as 
I have described represent what we may call an in- 
determinate law. Such expressions are sometimes 
called empirical laws, because they are really conven- 
tional expressions of the results of experiments, and 
can never be trusted far beyond the limits of the ex- 
perimental data. From another point of view these 
formulae may be regarded simply as methods of ap- 
proximation to indeterminate results. 



THREE CLASSES OF LAWS. 1 93 

Still, in discussing the nature and character of the 
laws of nature, these important modes of representing 
physical relations must not be overlooked, and they 
may be regarded as a third class of laws ; so that we 
have to distinguish the fixed laws, like the laws of 
motion, the determinate laws, like the lawof Mariotte, 
and the indeterminate laws, such as we have just de- 
scribed. That these last are in the fullest sense mere 
abstractions is sufficiently evident from what has 
already been said ; but after all, they do not differ 
essentially from the more determinate laws, as will 
appear from this final consideration. 

In those laws which can only be geometrically or 
algebraically expressed, we find the greatest differ- 
ences in the complexity of the relations which the 
curves or formulae exhibit; and sometimes the ex- 
pression is so simple that it might well be questioned 
under which of the two artificial categories we have 
made, the given relation should be classed. Between 
classes which thus blend there are not usually any 
essential differences, and such differences as we find 
probably depend on the greater or less complexity 
of the phenomena under consideration. The distinc- 
tion between the fixed and the variable laws appears 
to be more fundamental; and the first, as we have 
before said, seem to be expressions of the essential 
properties or relations of matter and energy. 

The conception of the distinction I have drawn as 
it exists in my own mind, may be readily illustrated 
by the well-known Jacquard loom, which with numer- 
ous modifications is used for weaving almost every 
kind of fabric having inwrought designs. In such a 



94 JACQUARD LOOM. 



machine, a carpet-loom for example, although the 
parts work in harmony, we may distinguish between 
the essential machinery of a loom common to all 
looms, and the ingenious devices of Jacquard by which 
the pattern is determined. Without these additions, 
the loom would weave a perfectly uniform plain 
fabric, with fixed and unvarying relations of the woof 
and warp ; but Jacquard's perforated cards determine 
a selection of the threads, and through a combination 
of these variable conditions, so complex that the ob- 
server cannot follow their intricate workings, the pre- 
designed pattern appears. 

So is it, as it seems to me, in the loom of nature. 
Mass and energy are the woof and warp, with their 
commingled tints, out of which the tissue of events 
has been woven ; and these fundamental relations are 
fixed and invariable. But ten thousand changing 
conditions, fore-ordained by Omniscience and di- 
rected by Unerring Wisdom, select the threads, and 
thus gradually the great design is unrolled. 

I might push the analogy further; but such simil- 
itudes are of value only as suggestions to thought, 
and I leave the subject to your reflections. 

From the very necessities of the case the analysis 
of the laws of nature, which I have given in this lec- 
ture. Is far from complete ; and I cannot, therefore, 
hope that it is conclusive. Only in proportion as 
one sees clearly is it possible to describe clearly what 
appears ; and when peering through a mist all out- 
lines are ill-defined. But such is the condition under 
which the investigator must work, and he can only 
tell you faithfully what he thinks he discerns. Some- 



EDUCATIONAL ASPECTS. I95 

times, however, the clouds break, and he gains a 
vision of the truth in its glory ; and I trust one con- 
clusion at least remains clear to you after this dis- 
cussion. 

From no point of view can the laws of nature be 
regarded as efficient causes ; and this ruler which a 
materialistic philosophy has attempted to enthrone 
over the universe is no potentate in any sense, but 
merely a very intangible, indistinct, and protean 
mental image of man's abstraction. 

As has already been intimated, this sophistry of 
materialism has been very widely disseminated in 
consequence of our imperfect methods of education. 
The only knowledge of material relations which most 
even of our educated people acquire is derived from 
elementary text-books, whose formal statements con- 
stantly convey false impressions; and hence arises 
much of the fallacy which prevails. It may not 
therefore be out of place to devote the remainder of 
the hour to a short discussion of the educational 
aspects of our subject. 

One of the most brilliant and influential writers of 
our day, while fully conceding the very great im- 
portance to the scholar of the general results of 
science, as furnishing an essential part of the ma- 
terials of modern literature, has expressed the opinion 
that the details and methods of science are of value 
chiefly to experts, and are unfit materials to form the 
basis of liberal culture. 

With the general spirit of Mr. Matthew Arnold's 
address on ** Literature and Science " (first delivered 
as the Rede Lecture at the University of Cambridge 



196 LITERATURE AND SCIENCE. 

in England, and afterwards often repeated in this 
country) I entirely sympathize. I freely admit that 
as a means of liberal culture that knowledge is most 
important which, to use Mr. Arnold's striking ex- 
pression, can be most directly related to the sense 
for beauty and the sense for conduct; as well as I 
should add to all the senses which make up that won- 
derful composite we call character. Character is the 
great end of education; and that which arouses in 
man elevated thoughts and conceptions, and that 
which stirs within him great resolves that lead to 
noble deeds, has more influence on character than 
any special knowledge however profound, and how- 
ever valuable in itself considered to the welfare of 
society. 

The term " science " was used by Mr. Arnold in its 
broadest sense, to include any body of systematized 
facts, whether of nature or of any department of 
human learning ; and I wholly agree with him that 
the mere acquisition of knowledge, however useful, is 
a very insufficient means of liberal culture ; and also 
that it is equally unimportant to the great mass of 
educated men whether the products of the combus- 
tion of a wax taper be carbonic acid and water, or 
whether the genitive plural oi pais and pas take the 
circumflex on the termination. The practice in so 
many of our schools of cramming immature minds 
with heterogeneous information, which they at least 
are unable to relate to the sense of beauty, to the 
sense of conduct, or to the sense of fitness of any 
kind, is to my mind a waste of golden opportunities, 
and productive of no permanent good. 



CLAIMS OF SCIENCE. 1 97 

But while conceding all this, I claim for the study 
of physical science, if rightly pursued, the highest 
value, even when judged by the very criteria which 
Mr. Arnold has so acutely laid down. The grand re- 
sults of physical science are most closely related to 
the sense for beauty, and to the sense for conduct; 
and as a matter of fact they have satisfied the needs 
of the noblest men for beauty, for conduct, — and for 
holiness also, — as fully as any earth-born knowledge 
ever can. The beauty of God's creation loses none 
of its loveliness to him who knows the fitness of all 
the parts. Beauty, as we have before said, is simply 
that harmony of proportions and qualities which re- 
sults from the most complete fitness of all the parts 
in a perfect whole, and becomes the more apparent, 
and the more commanding, in the exact proportion 
as that fitness becomes known and appreciated 
through study and investigation. His mind must 
be dull indeed whose noblest impulses are not awak- 
ened, and aroused to action, by the revelations of in- 
telligence and forethought which come from the 
study of the material universe; and we can aptly 
quote, though with a somewhat different interpreta- 
tion, the refrain of Mr. Arnold's noble address, — 
" no wisdom, nor understanding, nor counsel, against 
the eternal ! " 

Passing now for a moment from the subject matter 
to the methods of science, I may venture to assert, as 
the conclusion from an unusually long experience as 
a teacher, that no one can acquire an adequate 
knowledge of scientific results without such an ac- 
quaintance with the methods by which the results 



198 KNOWLEDGE OF METHODS ESSENTIAL. 

were obtained as will give a correct appreciation of 
the limitations under which the conclusions must be 
received ; and that in many cases no language, how- 
ever skilfully used, is adequate to convey an accurate 
conception of the truth. A student must observe 
and experiment for himself if he would acquire clear 
and correct ideas of natural phenomena. Every 
teacher of experience knows that the conceptions 
acquired from elementary text-books and popular 
lectures are constantly erroneous, and often absurd. 

Take such a simple result of chemistry as that 
water is composed of oxygen and hydrogen. I am 
sure from my own experience that not one in ten of 
the young men and women who learn to repeat this 
statement at our high schools and academies have 
any clear idea of what it means. For many years 
I have asked questions on the examination papers 
for admission to Harvard College to test this very 
point, and it has been the rarest exception to re- 
ceive an intelligent answer. Although I have re- 
peated the same question year after year, the result 
has been uniformly unsatisfactory; and not until ex- 
perimental teaching was introduced into some of the 
preparatory schools was there any improvement. 
To most of the men the names oxygen and hydrogen 
conveyed no conception of definite substances ; and in 
what sense it could be said that the familiar liquid 
water was composed of two aeriform substances, and 
on what evidence this remarkable scientific conclu- 
sion is based, almost no one had clear ideas. The 
laboratory student, however, who has actually made 
oxygen and hydrogen gases from water, and who has 



NATURE THE ONLY AUTHORITY. 1 99 

satisfied himself with this evidence that these aeriform 
products came from the material of water and from 
nothing else; who also has mixed two volumes of 
hydrogen gas with one volume of oxygen gas, and 
after exploding the mixture with an electric spark 
has seen that the result is two volumes of vapor 
which condense on cooling into liquid water, and 
must therefore be steam, — has a knowledge of a 
wholly different kind. He knows that the conclusion 
so tersely stated in his text-book is far from self-evi- 
dent; he has experienced the difficulties which had 
to be overcome before the truth was established ; he 
has seen the limitations under which this truth must 
be held ; and his knowledge is complete and final. 

In literature the printed record is the final appeal ; 
but in science books are at best only a secondary 
authority, and can never supply the place of direct 
observation and experiment. All descriptions of 
natural phenomena are necessarily partial and im- 
perfect ; and in elementary works they are as a rule 
so inadequate as to be constantly misleading. Any 
one who relies upon them is liable to be led into 
serious error. Hence it is that students of nature 
often hold in such slight esteem popular expositions 
of scientific subjects, feeling that they often convey 
false impressions and inculcate error in spirit, if not 
in substance. Nevertheless, such popular expositions 
have their proper place, and are of the greatest im- 
portance, not only by awakening interest in scientific 
subjects but also by exhibiting large views of scien- 
tific relations. They are avenues to knowledge which 
men may wisely follow, and by which many have been 
14 



200 EDUCATIONAL NEEDS. 

led into the sanctuaries of truth ; but the scholar must 
worship at the shrine and wait on the altars, if he 
would interpret the oracles aright. 

One of the great educational needs of our day is 
such a training by the schools in experimental 
methods as will enable the great body of our edu- 
cated men to weigh scientific evidence, and thus to 
protect the community from the frauds and sophis- 
tries of which otherwise intelligent, instructed, and 
even shrewd men are now so frequently the dupes. 
Of the common-school system, so early established 
and carefully fostered by our forefathers, we are justly 
proud ; but let us not be blind to the fact that this 
system has grave defects, and has been excelled in 
several countries whose governments entered on the 
great work of popular education long after ourselves. 
In many respects our methods of elementary educa- 
tion are inferior to those of Germany, of Sweden, or 
of Italy. Two very obvious reasons may be assigned 
for this result. In the first place, the details of our 
system are ordered by the average, and not by the 
highest intelligence of the community; and in the 
second place, our school boards are greatly hampered 
in all efforts for reform by the cost of labor. 

The ingenuity of our people has not failed to devise 
expedients for economizing the labor of the teacher, 
and thus for enabling one man to control the greatest 
possible number of pupils. In almost every subject 
taught in our secondary schools books are provided 
in which each day's lesson is exactly proportioned, 
and the questions to be asked definitely appointed. 
The teacher's work is made as mechanical as possible, 



MECHANICAL TEACHING. 201 

and the pupil's task becomes a mere exercise of the 
memory. Under such conditions there is no need 
that a teacher should have any special knowledge 
of the subject taught; and untrained persons are em- 
ployed, whose whole knowledge of the subject is 
bounded by the covers of a school-book ; which too 
often has been prescribed by a school committee, 
under the influence of interested pubhshers. Thus 
education is cheapened in our country, like so many 
other products of labor, at the expense of refinement 
and finish. 

It is no wonder that the overworked and under- 
paid teachers should oppose any change which neces- 
sarily involves a large increase of labor, even when 
they fully recognize the ruinous effects of the me- 
chanical system under which they are compelled 
to work. Obviously, however, this substitution of 
indiscriminate cramming, in place of intelligent acqui- 
sition is fatal to the efficiency of our school system, 
and a reform should be demanded at any cost. 

Fortunately, our political system is as flexible as it 
is crude; and if the demand is seriously made the 
reform is sure to follow. But let it be remembered 
that the changes required will be necessarily costly, 
and we must be prepared to bear the increased ex- 
pense. Do not, however, be deceived by any make- 
shifts which are often paraded as scientific education. 
If teaching is to be simply a process of loading the 
memory with more or less useful, as well as more or 
less ephemeral, information it makes little difference 
in the end what are the materials used in the process 
of cramming. The material may as well be the long 



202 CONDITIONS OF SUCCESSFUL TEACHING. 

list of exceptions to the rules of prosody, required in 
the Latin schools of former days, as descriptions of 
experiments in physics or chemistry so glibly recited 
by the pupils of our modern high schools. 

No teaching of science is of any value which is not 
a direct appeal from the mind of the teacher to the 
intelligence of the pupil. The teaching must be 
direct and personal, and this necessarily implies a 
large expenditure of time and patience, a special 
training on the part of the teacher, and a great 
increase of teaching force. 

The successful teaching of natural science also 
requires that the teacher should be independent of 
all books. The great object of science-training is to 
enable the scholar to interpret nature ; and the book 
of nature is the only text-book which should be pre- 
scribed. As in the study of ancient classics the one 
great aim is to acquire such a command of Latin or 
Greek, such a knowledge of the circumstances and 
relations of these elder nations, as will enable the 
student to render not only the general sense, but also 
the delicate shades of meaning and the coloring of 
the language of their writers; so in the study of 
science the great object is to interpret the meaning 
of natural phenomena, to decipher the significance 
of every feature, and to show forth the intelligence of 
which nature is the expression. 

Books have their value chiefly as guides, and as 
records of what has already been accomplished ; but 
in the study of nature they hold a secondary and 
subordinate, and not a chief place. To train young 
minds to interpret nature is a perfectly practical 



THE TRUE AIM. 203 



scheme. The power can be acquired as readily as 
the ability to translate Virgil or Homer, although of 
course with limitations which are similar in both 
cases ; and it is this power, and not the mere acqui- 
sition of scientific knowledge, at which the so-called 
" new education " aims. This all-important state- 
ment cannot be too often repeated, or too strongly 
emphasized. The advocates of an exclusively clas- 
sical culture constantly describe the new education 
as an attempt to substitute the acquisition of useful 
knowledge for mental discipline; or, at best, to re- 
place serious intellectual work with superficial object- 
teaching; and, as we have before intimated, there 
has been an attempt on the part of some schools to 
satisfy an obvious demand with such contemptible 
shifts. Let me then repeat that the great aim of sci- 
entific training should be the ability to interpret 
nature ; and that in large measure the acquisition is 
within the reach of every educated man, although 
in its higher manifestations the successful exercise 
of this ability may be a privilege of only the most 
gifted intellects. 

That such training is of the highest value and is a 
legitimate aim of education, must, I think, be univer- 
sally admitted; but it cannot be secured without 
trained teachers, without well-appointed laboratories, 
and except at a cost proportionate to such require- 
ments. Certainly we cannot afford to fall behind the 
most favored nations of the earth on the very ground 
which we first occupied ; and it is equally certain that 
no investment will yield a larger return than the money 
expended in the acquisition of real knowledge. 

The distinction between real knowledge and formal 



204 REAL AND FORMAL KNOWLEDGE. 

knowledge is one of paramount importance, which 
should never be overlooked in our plans of educa- 
tion. That knowledge alone is real to a student 
which is obviously related to some need of his life, 
or to some phase of his intelHgence. All other 
knowledge, however valuable in itself considered, is 
to him formal. Obviously, the distinction here in- 
sisted on is purely a relative one; for the same 
knowledge which is formal to one man may be very 
real indeed to his next-door neighbor. The para- 
digms of grammar are formal knowledge to the young 
student who memorizes them for the first time, but 
are very real knowledge to the grammarian. Even 
formal knowledge has its right place ; and there are 
exigencies under which its acquisition is to be en- 
couraged or even enforced. Man is a creature of 
habit, and his usefulness requires that certain essen- 
tial truths should become so woven into his nature as 
to be always at hand on every emergency. Certainly 
the multiplication-table and the spelling-book repre- 
sent formal knowledge of this sort; but I do maintain 
that it should be the great object of education to re- 
late all knowledge, so far as possible, to the pupil's 
understanding. 

I know that on this point I differ from many old 
experienced teachers whom I greatly respect. It was 
formerly held almost universally, and even now it is 
believed by many teachers, to be best for a child to 
acquire knowledge at first in a formal way, and to 
wait for the development of his intelligence to ex- 
hibit its relations. On this theory, boys preparing 
for college in my own school-days were compelled to 



REAL AND FORMAL KNOWLEDGE. 20$ 

learn the Latin grammar by rote before they under- 
stood the meaning of one half of the terms employed. 
The vivid remembrance of my own experience may 
lend undue proportions to this abuse of the memory ; 
still, after a long experience as a teacher myself, I 
cannot but regard such discipline as a great waste of 
mental energy, if not absolutely cruel ; and no one 
can deny that the acquisition of any knowledge is 
greatly facilitated when the relations of the knowledge 
are understood. I have granted that in certain cases 
the acquisition of formal knowledge is necessary; nev- 
ertheless, it should be the study of the teacher to les- 
sen the requirement as far as possible ; and certainly in 
science, formal knowledge is wholly without value. 

Some years ago, while working in the mineralogical 
cabinet under my charge at Cambridge, I was ad- 
dressed by two lady visitors who had evidently found 
great interest in the collection, and asked some very 
intelligent questions in regard to several of the more 
common mineral species. It gave me great pleasure 
to answer their inquiries, and I passed a pleasant 
hour in pointing out some of the characteristic feat- 
ures of quartz, feldspar, mica, pyroxene, hornblende, 
and similarly familiar minerals which are the constitu- 
ents of our common rocks. At the close of this im- 
provised lecture, one of the ladies said to me in an 
apologetic tone, — evidently deeming some excuse re- 
quired for such an unusual feminine taste, — " We are 

teachers In the High School," naming a town 

not one hundred miles distant from Boston, '^ and I 
have been taking a class through the sections on 
mineralogy, introductory to Dana's Geology; and I 



206 REAL AND FORMAL KNOWLEDGE. 

was interested to see some of the minerals described 
in them." 

I think this incident, without further comment, will 
illustrate what I mean by a formal knowledge of ele- 
mentary science, and will also show how utterly worth- 
less all such acquisition must be. The incident has 
an amusing side, but it also exhibits a very sad aspect 
of our secondary education. This lady was evidently 
a conscientious teacher, who had a conception of 
something better than the mechanical routine in which 
she was forced to work, and this had led her to seek 
some real knowledge of the subject she had to teach. 
I know that there has been a great improvement in 
our schools during the last few years ; and the prac- 
tical classes supported by the Lowell Fund, under the 
direction of the teachers of the Boston Institute of 
Technology, as well as similar courses under the aus- 
pices of the adjacent Natural History Society, have 
done not a little to hasten the reform. But our best 
teachers are still constrained by over-crowded class 
rooms, and the mechanical routine which this condition 
of things necessarily implies. Of this I know. There 
is not a more devoted or more conscientious class of 
workers in our community than the teachers of the 
secondary schools; and if our people realized how 
much mental energy was wasted in these schools by 
just such senseless tasks as attempting to teach min- 
eralogy from a book, the teachers would soon be 
relieved from such profitless and thankless duties. 

What I have said in regard to the teaching of 
science, applies with almost equal force to literary 
studies as well. Real knowledge has the same great 



REAL AND FORMAL KNOWLEDGE. 20/ 

worth in every department of learning, and formal 
teaching the same deadening influence; and let it 
not be inferred from anything I have said, that I 
desire to exalt scientific culture at the expense of 
literary or artistic culture of any kind. All mental 
culture is alike good ; and it is not by a one-sided 
growth, but by a symmetrical development of all its 
powers, that a community can secure the largest 
productiveness and acquire the widest influence. 

I have elsewhere expressed myself so strongly on 
this point that it does not seem to me necessary that 
I should guard the language here used against any 
misinterpretation ; but that I may make the dec- 
laration still more emphatic, let me repeat that I 
still believe the old forms of literary culture to be 
for the large majority of scholars the best prepara- 
tion for useful lives. I merely claim that there is an 
important class of the students who now seek a col- 
lege education, for whom, on the other hand, a sci- 
entific culture will best secure their future usefulness ; 
and I have already indicated sufficiently clearly what 
I mean by scientific culture in this connection. Let 
not scientific culture be confounded with technical 
training, and let it not be misjudged by any counter- 
feits which have assumed its name. Several of the 
sciences have opened lucrative fields for professional 
labor; and the engineer, the chemist, and the electri- 
cian follow as learned vocations as the lawyer or the 
physician. For each of these new professions, as 
for those of the elder triad, special training is re- 
quired; and in all of them some of the subjects 
involved are the same as those studied in view solely 



208 TECHNICAL TRAINING AND LIBERAL CULTURE. 

of a general education. The difference between 
technical training and liberal culture depends, not 
chiefly on the subject-matter studied, but on the 
purposes and spirit with which the study is pursued. 
Thus, chemistry studied with the object of manufac- 
turing chemical products, or of directing other chem- 
ical industries, or of solving the numerous sanitary 
and technical problems which constantly arise in 
every highly civilized community, is a legitimate 
and learned profession; but when studied for the 
sole object of interpreting nature and extending 
knowledge, it is one of the liberal arts. I do not 
say that one object is more worthy or more noble 
than the other ; but I do maintain that any country 
becomes more enlightened and more honored in 
proportion as liberal culture is fostered and main- 
tained. That it will have its proper place in our 
community is already assured ; and the movement 
recently inaugurated by Harvard College is already 
producing visible effects. 

To this reform in education, and to the substitu- 
tion of real for formal knowledge which it involves, 
I look more than to anything else for the reconcilia- 
tion between science and theology. When all the 
wisdom and learning of this world has been related 
not only to man's need of beauty and to man's need 
of conduct, but also to man's need of understanding 
and man's need of religion, the harmony between 
material and spiritual truths will plainly appear; and 
thus it is that this discussion of what seemed at first 
a purely educational problem, has an important 
bearing on the larger subject we have in hand. 



THE MEANING OF LAWS. 209 



LECTURE Vlir. 

THEORIES OR SYSTEMS OF SCIENCE. 

IN my last lecture I defined a law of nature as a 
declaration or statement of a certain order, se- 
quence, or relation observed among natural phenom- 
ena, and aimed to show that such propositions could 
be regarded from no point of view as efficient causes. 
It is not in the study of nature alone that the mind 
of man does not rest satisfied with laws. In social 
relations as well as in science, men demand to know 
the meaning of laws, and their demands are the more 
imperative in proportion as they become more en- 
lightened. The scientific investigator is not con- 
tent with a knowledge of the outward relations of 
phenomena. He seeks to discover the proximate 
causes of the order he has observed, and although 
he may not be able to reach certainty, he is not 
satisfied until he has framed some explanation by 
which he can classify his facts, and which at the same 
time will give the form and body to his thoughts 
so indispensable for successful study. Hence arise 
of necessity the hypotheses, theories, and systems of 
science. 

Using the term in its broadest sense, an hypothesis 
is a postulate imagined or assumed to account for 



210 HYPOTHESIS. 



what is not understood. Its derivative meaning from 
viroOeo-L^i (a supposition) is closely followed in the 
meaning here assigned to the word. These suppo- 
sitions may be based on a larger or smaller knowl- 
edge, they may be more or less in harmony with nat- 
ural phenomena, they may more or less fully agree 
with generally accepted systems of science ; but they 
differ from the laws of nature in that they seek to go 
behind the external relations of things, and explain 
how this order might have been produced. The 
word " hypothesis," unfortunately for our purpose, 
has acquired a coloring which suggests a deprecia- 
tory inference. A plausible supposition is sometimes 
spoken of contemptuously as " a mere hypothesis ; " 
and possibly for this reason the term ** theory," al- 
though often branded in a similar way, is frequently 
used by scientific writers to distinguish such hypoth- 
eses as they regard as more credible or more fully 
established. But until the truth of an hypothesis 
has been placed beyond doubt, — when of course it 
ceases to be a supposition, and is classed among 
fixed facts, — the degree of credibility must be to a 
great extent a matter of opinion, and no definite line 
of distinction can be drawn. Moreover, the word 
" theory " has a very important use, corresponding 
also to its derivation, which we cannot afford to have 
compromised. We shall use, therefore, the word 
" hypothesis " to designate any assumed explanation 
of natural phenomena, without any implication as to 
the plausibility of the supposition. 

As is well known, it is a fundamental doctrine of 
the positive philosophy that man can know nothing 



man's discernment, and god's inspiration. 2 1 1 

of efficient causes. Hence all hypotheses are vani- 
ties, and the only reasonable course for helpless man 
is to limit his attention to determinate relations of 
phenomena ; that is, to natural laws. But this phil- 
osophy utterly ignores the only power by which the 
level of human knowledge can be raised ; that is, in- 
duction : and as we have shown in previous lectures, 
the whole history of science is simply the story of 
verified inductions. Guesses at truth are not to be 
despised, for they have been again and again divina- 
tions. 

We cannot expect fruitful suggestions except from 
men who are thoroughly acquainted with the subject 
they are studying; but to gain any insight into 
nature's processes, something more than erudition is 
required; call it genius, call it intuition, call it in- 
spiration, or by whatever other name, there is an 
element, although we may not be able to define it 
precisely, which we all recognize in such creative 
minds. Man's discernment and God's inspiration 
blend together, and no one can distinguish the point 
where they meet. 

There is a certain sense in which the suggestions 
of gifted minds may be said to be the oracles of God ; 
and there is another sense in which they m.ust be 
regarded as the conceits of very fallible and short- 
sighted men; and it is no wonder that their value 
will be very differently estimated according as they 
are regarded from one or the other point of view. I 
have the greatest respect for the love of truth and 
accuracy which the positive philosophy so strongly 
inculcates ; but, as it seems to me, this doctrine finds 



212 SYMPATHY BETWEEN MIND AND NATURE. 

its chief disciples among scholars who have been so 
engrossed in deductive methods as to overlook the 
mental visions by which the broader relations of truth 
have been discovered. 

To my mind there is a deeper and nobler philoso- 
phy than positivism, which explains that mysterious 
sympathy between mind and nature so evident in the 
great discoverers, — a philosophy proclaimed in the 
declaration of Holy Scripture that man was created 
in the image of God. Only in proportion as man par- 
takes of the Divine intelligence can he understand the 
Divine creation, and just in proportion as he is in 
sympathy with the Divine mind will he recognize the 
Divine thought which has been manifested in nature. 
And even if we take no higher view than that man 
has grown into harmony with his environments 
through the influence of what is called natural selec- 
tion, we must at least recognize in such antecedents 
a close relationship with the rest of nature ; and this 
affinity alone would help to explain the power of 
genius to frame fruitful hypotheses. 

As we have already explained, there is but one sat- 
isfactory test of the Divine afflatus in such imagin- 
ings ; and that is the test of experience. Hypothesis 
is of value only in so far as it explains facts, and by 
pointing out consequences directs investigation, : — as 
has been already fully illustrated. In this way hypo- 
theses have been the chief means by which science 
has been advanced. The great discoverers have been 
the men who were the most fruitful in hypotheses, 
and at the same time most skilful and conscientious 
in submitting them to the test of observation and ex- 



THEORIES OF SCIENCE. 213 

periment, — men like Copernicus, Kepler, Galileo, 
Huygens, Newton, Oersted and Faraday. 

I have already shown out of what copious and often 
grotesque fancies the laws of Kepler were educed ; 
and Faraday, although far more sober-minded, was 
equally distinguished by exuberance of fancy; but, 
like Kepler, he submitted his hypotheses to the 
severest tests. So also Newton, while emphatically 
expressing his contempt for idle speculations in his 
celebrated aphorism already quoted, constantly made 
use of legitimate hypotheses in his own investiga- 
tions, — as both his ** Optics " and his " Principia " 
give abundant evidence. 

The word " theory " — from decopeco, to see or con- 
template — is correctly used in speaking of a system 
of science, as the theory of music, or the theory of the 
moon; and to this meaning it is best limited. In 
this sense a theory may involve many principles and 
complex relations. It may be based on known laws 
or definite facts, as is," for example, the theory of 
sound ; or it may rest to a greater or less extent on 
hypotheses, as does the undulatory theory of light on 
the assumption of an adamantine ether. It is there- 
fore plainly to be distinguished on the one hand from 
a law, which is the declaration of known relations, and 
on the other hand from an hypothesis, which is an 
assumption of unknown conditions. Indeed, it often 
includes both laws and hypotheses, and attempts to 
correlate them in a consistent system. The theories 
of science are of the very greatest value, and chiefly 
in two ways. 

In the first place, a good theory has a very great 



214 VALUE OF THEORIES. 

educational value. It classifies facts, it unfolds phe- 
nomena in logical sequences, and exhibits events in 
intelligible relations. As thus presented, the mind is 
able to grasp the subject as a whole, to view it in 
many relations, and through their relationships to 
gain a command of a mass of facts which otherwise 
the most retentive memory could not hold. We are 
all acquainted with this use of theory. We know 
how completely our working knowledge in almost 
any department of learning is associated with the 
system in which it was acquired, and many of us 
know by experience how difficult it is to work with a 
new system when the progress of knowledge demands 
a change. Theories are thus necessities of our men- 
tal constitution, and essential conditions of effective 
thought. 

In the second place, theories are of the very great- 
est use in directing investigation, and in natural science 
their efficiency in this respect is their chief merit. 
The highest recommendation we can give to a system 
of science is to say that it is a good working theory ; 
and in saying this we do not necessarily pass any 
judgment on the credibility of the system as abstract 
truth. As I shall soon show, we have good working 
theories whose postulates cannot for a moment be 
regarded as realities; but so long as the theories 
direct us to new discoveries it would be the height of 
folly to abandon them simply because they cannot be 
squared with our speculative philosophy. There has 
been a great deal of misunderstanding on this point 
which, in the interest both of religion and of sound 
philosophy, ought to have been avoided. Sober- 



RESERVATION OF JUDGMENT. 215 

minded men have been accused again and again of 
being false to religion because they entertained theo- 
ries which the Church at the time regarded as incon- 
sistent with sound doctrine ; and, in defending their 
position, I have known men of great power driven 
into extreme positions by an intolerance which forced 
a mental conflict where none need to have followed. 
If in the study of nature there is one truth more than 
another which it is important for the student to learn, 
it is that in a great many cases reservation of judg- 
ment is the only honest attitude of the mind ; and 
that man is to be honored, and not persecuted, who 
can use his theories for what they are worth and 
keep his faith in eternal verities pure and radiant. 

As we cannot expect a theory fully to harmonize 
with our philosophy, so we cannot expect that its 
predictions will always be verified. Of course the 
failure of a theory to account for well-established 
phenomena shows that either the theory or our 
powers of deduction must be at fault ; but this is no 
reason for rejecting the system, until we can find a 
better theory to take its place. How foolish it would 
have been for Columbus to throw overboard his com- 
pass-needles when he discovered that they did not 
point exactly to the north star. Like all human in- 
ventions, systems of science are imperfect; and we 
must accept them for what they are worth, and use 
them only so long as they give us essential help in 
our search for knowledge. It has been repeatedly 
the case in the history of science, that theories have 
failed so completely to do their legitimate work that 
they have been deposed and new theories enthroned 
15 



2l6 HYPOTHETICAL MAGNITUDES. 

in their place; but so intimately are theories asso- 
ciated with our processes of thought, that the change 
has usually been attended with an intellectual revolu- 
tion. As I have shown in these lectures, it was so 
when the Ptolemaic theory was set aside ; and we 
have had a similar experience in chemistry since I 
have been a teacher of the science. 

We have said that a system of science might in- 
volve postulates wholly inconsistent with sound phil- 
osophy, and yet remain a good working theory; we 
have now to add, what is still more surprising, that 
such a theory may give us accurate measurements of 
magnitudes which are wholly hypothetical, and of 
whose relations we have otherwise no positive knowl- 
edge. Such, for example, are the absolute lengths 
of the so-called waves of light, and the relative 
weights of the chemical molecules and atoms. There 
cannot be a question that the values obtained are 
real magnitudes; and, although we have made our 
measurements in the dark and have not known cer- 
tainly what we were measuring, yet the definiteness 
of the results gives us the strongest assurance that 
our theories contain an element of truth, although the 
truth may be clothed with much error. 

We have already seen what a mighty influence the 
Ptolemaic system and the *' Organon " of Aristotle 
exerted over the intellectual world for more than a 
thousand years ; and at the present day, besides the 
many subsidiary theories, there are four great systems 
of science which possess a similar authority. These 
are the Theory of Universal Gravity, the Undulatory 
Theory of Light, the Molecular Theory of Chemistry 



DOMINANT THEORIES OF SCIENCE. 21/ 

and Physics, and the Theory of Organic Develop- 
ment; and I propose in this lecture to show that 
these famous systems of science exhibit in a most 
striking manner the characteristic features of all 
human theories to which I have referred. 

In my last lecture I not only pointed out the clear 
distinction between the law of gravitation and the 
theory of universal gravity, but I also discussed some 
of the incongruities which this assumed mode of 
action presents, showing that the idea of independent 
attractive forces exerted by separate particles of mat- 
ter was not only inconsistent with the fundamental 
conception of inertia, but also entirely out of har- 
mony with our knowledge of other attractive forces, 
like those exerted by electricity and magnetism. 
Remember that each particle of matter of this earth 
is assumed to attract each particle of the planet 
Jupiter, each one every other, as if there were no 
other material in the universe. 

Now besides the improbability and incongruity of 
such independent action, the whole idea is at utter 
variance with a principle which in all philosophical 
thought has always been regarded as a prime condi- 
tion of every mode of action, and which is expressed 
in the aphorism " Nulla actio in distans." This prin- 
ciple has been universally recognized in other systems 
of science. It was recognized by Newton himself in 
his emission theory of light, which ascribed the lumi- 
nous power to small projectiles darting through the 
intervening space and carrying the energy from the 
luminous body to the point of application; and to 
these projectiles Newton gave form and imparted ro- 



2l8 THEORY OF UNIVERSAL GRAVITY. 

tation in order to explain what he called " fits of easy 
transmission " or reflection. The same philosophical 
necessity for a medium of transmission led Huygens, 
in framing his wave theory of light, to fill all space 
with an elastic medium, through which the waves might 
be propagated. This medium, which to his conception 
was an indefinitely attenuated but highly elastic con- 
dition of aeriform matter, as its name denotes, the de- 
mands of modern science, as we shall soon see, have 
converted into an adamantine solid. It was again the 
same necessity of thought which, in a most memo- 
rable investigation, led Faraday to search for the 
medium through which electrical attractions and re- 
pulsions are exerted, and to distinguish, as he did 
with so much skill, the qualities and relations of the 
dielectric. While, however, we have met the neces- 
sity by interposing a medium through which a par- 
ticle of sodium at the sun sends to our spectroscope 
an intelligible signal, that same particle is assumed 
by the theory of gravitation to exert an attraction on 
every particle of that instrument at the distance of 
ninety millions of miles, not only independent of any 
medium, but also irrespective of any conditions or 
relations except mass. 

Although I feel strongly the philosophical objec- 
tion to the theory of gravitation which I have en- 
deavored to present; and although I feel under the 
constraint of the same limitations of thought to 
which I have referred, — yet sometimes I cannot but 
fear that we are influenced by the old aphorism more 
than we ought to allow ourselves to be; and that, 
after all, we may be but repeating the experience of 



NULLA ACTIO IN DISTANS. 219 

the Aristotleans at the time of Galileo. Who can 
question that Nature's abhorrence of a vacuum was 
as much a philosophical necessity to them as ** Nulla 
actio in distans " is to us. Man cannot act where he 
is not, or where he cannot reach, — although the elec- 
trical nerves of modern science enable him to reach 
across oceans and continents, and almost even to 
clasp the globe itself. Moreover, on the earth we 
cannot transmit energy without an adequate medium. 
The falling water acts directly on the turbine, but 
power cannot be transmitted from this water-wheel 
to the spindle and looms except through adequate 
shafting, pulleys, and belts. So also the power of 
steam, however far the steam may be carried through 
pipes, must do its work ultimately against the piston 
of the motor. Even the more modern dynamo- 
machine, by which power can be transmitted to 
greater distances than by any other means, must 
have a line of electrical conductors through which 
the energy passes. In all these cases power is lost 
in the transmission in such a way as to show that the 
transmission takes place from point to point along 
the line. All such analogies give a strong support 
to the doctrine that no action can take place except 
between contiguous masses; but should we not be 
careful not to limit in our thoughts the possibilities 
of nature by our own experience? It seems to me 
that such an attitude of the mind is required by 
philosophical sobriety; and although I have given 
a very different interpretation to the seeming non- 
conformity, it is possible that gravitation is the first 
exceptional phenomenon which has shown the short- 



220 UNDULATORY THEORY OF LIGHT. 

sightedness of our philosophy. Still the main fact 
which I have been endeavoring to illustrate remains. 
This grand theory of universal gravitation, from 
which has been developed the wonderful deduc- 
tions of modern astronomy, presents anomalies which 
our philosophy has been wholly unable to reconcile. 

Of the four great theories of modern science, the 
one which is to me the most fascinating is the un- 
dulatory theory of light. As a student of crystallo- 
graphy and of crystal optics, I have been charmed 
by the completeness with which it not only explains 
the general order of these phenomena, but also pre- 
dicts the magnitude, intensity, and other relations of 
each minute detail. Moreover, the remarkable pre- 
diction of conical fraction first made known on theo- 
retical grounds by Hamilton, and afterwards verified 
by Lloyd, will always be cited as one of the most 
striking examples of the prescience of physical sci- 
ence. Nevertheless, in spite of all its elegance and 
efficiency, the undulatory theory of light is imperfect, 
and demands postulates which even the wildest im- 
agination cannot reconcile with common-sense. 

The earlier exposition of the undulatory theory 
was published by Huygens nearly contemporane- 
ously with that of the emission theory by Newton ; 
but although from the first much more elegant in 
mathematical form, the theory of waves did not for 
a long time acquire nearly as great authority as the 
theory of corpuscles ; and even down to the middle 
of this century the two theories were described as 
rival systems in most text-books on optics. Sir 
David Brewster; one of the most successful students 



NEWTON AND HUYGENS. 221 

of optics in this century, who died in 1868, defended 
the Newtonian theory to the last Unquestionably, 
the paramount authority of Newton in astronomy 
gave greater weight to his hypothesis in optics than 
it intrinsically merited ; for there are not to be 
found in the whole history of science more elegant 
demonstrations than those which Huygens originally 
gave, deducing the fundamental principles of optics 
from the theory of the wave motion, — such principles, 
for example, as the rectilinear path of a beam of 
light, the laws of reflection and refraction, and above 
all, the phenomena of double refraction, then recently 
observed by Erasmus Bartolinus in Iceland spar. 

Huygens was undoubtedly led to his wave theory 
by the analogy which the phenomena of light and 
sound exhibit, and conceived of waves of light as 
transmitted like waves of sound in the atmosphere, 
only through a vastly more attenuated, but at the 
same time more elastic, medium which he called the 
" luminiferous ether." But in an aeriform medium, 
elasticity, the force by which waves are transmitted, 
can be developed only by compression. Of course 
compression at one point must be attended by expan- 
sion at contiguous points, and waves of sound consist 
in alternating states of compression and expansion 
spreading from every centre of disturbance. Such 
alternating conditions must produce variations of 
pressure at the surfaces which the medium touches, 
and the phenomena of wave motion result from the 
concurrence or interference of such partial effects, as 
Huygens so beautifully showed. 
- Although the general order of the appearances 



222 OBSERVATION OF MALUS. 

observed in the double refraction of light by Iceland 
spar was beautifully explained by the wave theory of 
Huygens, yet there remained certain features of this 
striking phenomenon — described both by Huygens 
and Newton — which were inexplicable until in i8io, 
when Malus, while looking through a double refrac- 
ting prism at the light of the setting sun reflected 
from the windows of the Luxembourg Palace at 
Paris, first observed the most fundamental of that 
remarkable series of phenomena which he afterwards 
developed and referred to what he called the ** polar- 
ization of light." Malus, who was a disciple of the 
emission theory, ascribed all these effects to a po- 
larity in the light-bearing corpuscles; and hence 
arose a name which is meaningless, and indeed con- 
fusing, on the basis of the theory of undulations. 
As soon, however, as the new facts came to be 
studied in the light of the undulatory theory, it was 
seen that the essential feature of the condition which 
had been called "polarization" was the transmission of 
the luminous energy in a definite plane ; and that the 
elementary motions in that plane which constituted 
the wave motion must take place at right angles to 
the direction of the rays of light. These considera- 
tions led to a profound alteration of the wave theory, 
first recognized by Thomas Young, but afterwards 
worked out with great ability by Fresnel. The wave 
motion could no longer be regarded as transmitted 
through an attenuated gas by the elasticity of com- 
pression, and it became necessary to conceive of the 
ether with parts held in definite relative positions, as 
in a solid, through which the waves are transmitted 



ETHER OF SPACE. 223 

by the elasticity of tension. In a word, the theory 
now filled space with an attenuated solid, whose 
parts are bound together far more firmly than those 
of steel. 

Consider now the apparently contradictory quali- 
ties which it has been found necessary to attribute to 
the ether of space, in order to explain the known 
phenomena of light and heat. In the first place, as 
the ether does not give rise to any sensible perturba- 
tions in the motions of the heavenly bodies, we must 
assume that it has no perceptible mass ; so that a solid 
block of ether of the size of this room cannot weigh 
more than a fraction of a grain. But while having 
such an excessive tenuity, we must in the next place 
assume that this singular solid consists of parts 
bound together with such an incredible force that, 
as the waves in passing through this medium tend to 
part or force together the ultimate particles, the ac- 
tion and reaction over each inch of surface must be 
measured by millions on millions of pounds. 

Why it is necessary to ascribe such an incredible 
elasticity to the luminiferous ether will in general ap- 
pear from two considerations. In the first place the 
immense velocity of light requires this great elasti- 
city. Assuming that two media have the same den- 
sity, their elasticities are proportional to the squares 
of the velocities with which a wave travels through 
them. The velocity of the sound wave in air is i lOO 
feet a second, or about one fifth of a mile, and that of 
the light wave about 183,000 miles a second, or 
nearly one million times faster; so that in proportion 
to its density the ether must have an elasticity a mil- 



224 TRANSMISSION OF POWER. 

lion million times greater than air. In the second 
place, this great elasticity is required in order to trans- 
mit power from the sun. The earth is but one of a 
number of great machines which are run by the sun. 
There is no form of energy manifested on the earth 
which cannot be traced to. the sun. The sun is the 
great motor from which all this power comes, just as 
directly as the power which runs the spindles and 
looms of a manufactory is transmitted by shafts, pul- 
leys, and belts, from a turbine wheel in the basement. 
Now these connections must be strong in proportion 
as the power to be transmitted is great ; and so the 
ether which transmits the power from the sun must 
be strong enough to do the work ; and if you reduce 
the material in it to next to nothing you must make 
what is left proportionally strong, — that is, ascribe to 
it this immense elasticity. Of course the imagination 
knows no bounds, and you may ascribe to the ether 
any extravagant relations you please; just as you 
can imagine materials so strong that the power of 
Niagara could be transmitted with shafts no larger 
than wires, and belts no larger than horse-hairs. 
And if you are not to take into any account the har- 
monies of nature, one supposition is as reasonable as 
the other. 

It is not, therefore, without reason that, following 
the authority of Jevons, I have called the luminifer- 
ous ether an adamantine solid ; and yet in the midst 
of this adamantine mass we live and move without 
perceiving the least resistance. In general two ex- 
planations have been given to show how motion in 
such a solid medium is possible. In the first place, it 



A SEMI-LIQUID. 225 



has been suggested that the molecules of a body 
may pass between the ultimate particles of the ether ; 
just as a flock of birds, regarded as constituting one 
mass, would pass between the branches of a forest, — 
the body not displacing the ether but, as it were, pene- 
trating it. I need not say that besides the difficulties 
of conception, there are insuperable philosophical 
objections to this view. The second suggestion is 
that the ether is a semi-liquid, which, hke pitch or 
ice near the melting-point, has a great elasticity as- 
sociated with an equally great degree of liquidity. 

Ice, as is well known, flows down-hill in the glacier's 
streams ; and so will pitch, although masses of either 
substance have marked elasticity, and will break with 
a conchoidal fracture like glass. Now conceive of 
the ether as pouring round a body, passing through 
it, without a parting of the ultimate particles of the 
medium, which continue to cling together with the 
immense force I have mentioned, — and you have 
the most recent conception that has been advanced 
of the relations of this inconceivable material. But 
obviously, such devices of the imagination do not in 
the least degree remove the difficulty of the concep- 
tion. Fundamentally, this difficulty consists in asso- 
ciating great extremes of qualities which from our 
experience seem to be incompatible. In ice or pitch 
a very small degree of liquidity is associated with 
elasticity of tension ; but in similar semi-Hquids the 
elasticity diminishes in proportion as the liquidity in- 
creases, while in the ether we are asked to associate 
indefinitely great elasticity with indefinitely perfect 
liquidity. 



226 IRRECONCILABLE RELATIONS. 

Such utterly incongruous and irreconcilable rela- 
tions may not discredit a theory as a system of sci- 
ence, but they must shake our faith in its credibility as 
a reality of nature. As we have already said, there is 
nothing in science so improbable, or so inconceivable, 
that it may not be realized. With all the unknown 
relations of nature it is not safe to say that anything 
is impossible, unless it absolutely conflicts with funda- 
mental laws. We are doubtless safe in expressing 
the opinion that no form of matter or energy can be 
produced without a corresponding expenditure ; and 
that those who stake ventures in processes for making 
materials or obtaining work from nothing are de- 
luded ; but much further than this it is not safe to 
prophesy. It is within our own experience that 
steam navigation, ocean telegraphy, and electrical 
lighting, were pronounced impracticable by men of 
large knowledge and great intelligence ; and we have 
lived to witness their confusion in the accomplished 
results. 

In all such cases, however, when the improbable 
has been once realized, it has been found to be in 
harmony with the rest of our knowledge ; and it has 
been seen that the seeming incongruity arose from 
our ignorance of general principles, or other links 
through which the relationship became evident. 
Therefore, while repeated experience of this kind 
should make us cautious, it cannot but increase our 
confidence in the general trustworthiness of the anal- 
ogies by which the student of nature is so greatly 
guided. But the same experience should also make 
us duly sensible of the limitations of our knowledge, 



A REAL CORRESPONDENCE. 22/ 



and inculcate largeness in thought and reservation in 
judgment. 

That such an adamantine medium as the ether of 
our theories actually exists I cannot for a moment 
believe ; but that the ether is our crude conception 
of some reality which bridges the celestial spaces I 
have no question. Perhaps in time the fulness of 
knowledge will come; perhaps it is incomprehensible 
to our limited faculties ; but that there is something 
corresponding to the ether of our imaginings, I feel 
as confident as that there is a solid crust of earth 
under my feet. In some way illimitable power 
crosses the immense gulfs of space; and what we 
catch glimpses of in the darkness, and try to express 
in our material symbols — whose inadequacy appears 
in the extravagances of our theories — is simply an 
order of being recognized as fully in the infancy of our 
race as now ; and of which it may be said as in the 
days of Job : " Where is the way where light dwell- 
eth? . . . Knowest thou the ordinances of heaven? 
Canst thou set the dominion thereof in the earth?" 

It is undoubtedly in consequence of the large ele- 
ment of truth which the great systems of science 
contain, in spite of all their philosophical absurdities 
and formal inconsistencies, that they have led us in 
several cases to a knowledge of magnitudes which, 
although entirely beyond our powers of direct obser- 
vation, have been measured with the greatest accuracy. 
In the undulatory theory this is true in regard to 
the lengths of the waves of light ; and although there 
is such large room for doubt in regard to the nature 
of these magnitudes, our knowledge of their values is 



228 WAVES OF LIGHT. 

SO exact that it has been seriously proposed to use 
them as standards of linear measurement. Remember 
that the longest of the luminous waves only measure 
1-39,000 of an inch — counted as with a water-wave 
from crest to crest — and you can see what such a 
proposition implies, and also what must be the order 
of the unknown quantity which we are able to meas- 
ure so accurately. And not only do we know the 
values of those magnitudes, but we have followed out 
their relations through most intricate conditions, and 
found our deductions most completely verified at 
every step of our inquiry. That these values are 
the magnitude of real things, we can have no more 
question than that the measurements given by Piazzi 
Smyth, in his work on the Egyptian Pyramids are 
the dimensions of actual blocks of stone, however 
much archaeologists may question this learned as- 
tronomer's theory in regard to the purposes for 
which these blocks were originally wrought. 

But besides presenting in its postulates the philo- 
sophical and formal incongruities I have pointed out, 
the undulatory theory is by no means perfect in its 
appropriate relations ; for there is a most important 
and conspicuous class of optical facts which it has 
as yet essentially failed to explain. I refer to the 
beautiful phenomena on which spectrum analysis is 
based. Newton's earliest experiment, in which he 
separated the colored rays composing white light 
by means of a glass prism, still challenges the 
undulatory theory. I have already referred to the 
remarkable investigation of Cauchy on this very 
point, which has been justly regarded as a monument 



THE DISPERSION OF LIGHT. 229 

of mathematical skill; but this investigation wholly 
failed in its main purpose. The most that Cauchy 
accomplished with his profound mathematical anal- 
ysis was to show that such effects might follow from 
wave motion on certain assumptions in regard to 
the molecular structure of the dispersing media; so 
that when our knowledge of molecular structure is 
more complete, the undulatory theory may possibly 
be able to explain the phenomena in question. He 
did not in any proper sense bring the phenomena of 
dispersion under the control of the theory; and to 
the average student they remain to the present day 
as inexplicable as ever. If, however, Cauchy's anal- 
ysis gives us good reason for expecting that with 
larger knowledge we may be able to include the 
phenomena of dispersion in our system, there are 
also equally strong grounds for the opinion that 
before this can be done the present undulatory 
theory must be profoundly modified. 

I fear that in thus dwelling on the inconsistencies 
and imperfections of the undulatory theory, it may 
seem as if I were aiming to discredit the system ; 
when on the contrary I desire to exalt it. The last 
word has always such undue force that, to avoid mis- 
apprehension, it is almost necessary to reiterate the 
opinion I expressed at first, — that the undulatory 
theory of light is one of the noblest creations of 
science, one of the greatest achievements of the 
human intellect, and that Its value can not be over- 
estimated. I believe that the system is no more 
imperfect than is necessarily implied in saying that 
it is a product of human thought, that it involves 



230 THE MOLECULAR THEORY. 

human conceptions, and must necessarily be subject 
to human limitations. My aim has been to exhibit 
the system in its true relations, and to show that we 
must be content to use it for what it is worth, and 
not expect to reconcile it at all points with either 
our speculative opinions or our limited experience. 

We come now to the third of the three great sys- 
tems of science which we have called the Molecular 
Theory, and this presents two very distinct aspects, 
according as we study the theory from a physical 
or from a chemical standpoint. On certain features, 
however, both the physicists and the chemists agree. 
By students of both classes the mass of material 
bodies is regarded not as uniformly and continuously 
distributed through the spaces they seem to occupy, 
but as segregated into an innumerable number of 
excessively minute masses called ** molecules," each 
of which is a separate unit, — as much so as a planet. 

There must be as many different kinds of molecules 
as there are distinct substances, but all the molecules of 
the same substance — as, for example, the molecules 
of water — are assumed to be the exact counterparts 
of every other. Of the absolute size of the molecules 
we can only form a very rude estimate, but the esti- 
mates made in different ways quite closely agree, and 
a conception of the order of magnitudes with which 
our theory deals is best given by means of the illus- 
tration already cited, which we owe to Sir William 
Thompson, who said that if a drop of water were 
magnified to the size of the earth, and the molecules 
of water magnified in the same proportion, they 
would certainly appear larger than ** marbles," and 



HEAT A MODE OF MOTION. 23 1 

smaller than cricket-balls. Wonderfully small as 
these niagnitudes must be, the theory does not on 
this account present any insuperable difficulties of 
conception ; for it only asks us to believe in a micro- 
cosmos beneath us, in some measure comparable 
with the macrocosmos which astronomy has shown 
to exist above us. The difficulties appear when we 
come to consider the attributes and relations which 
our theory compels us to ascribe to these minute 
masses. 

In physics the molecules are regarded as the 
points of application of forces ; as for example, when 
a body is expanded, melted, or volatilized by heat. 
Indeed, limiting our attention in this direction to 
thermal phenomena, heat itself is regarded as mo- 
lecular motion, and it is an established fact that a 
given quantity of heat corresponds to a definite 
amount of mechanical work. On the molecular 
theory, quantity of heat means simply quantity of 
molecular motion, and' temperature is the average 
moving energy of individual molecules. Molecular 
and mechanical motion are interchangeable. When 
a cannon-ball strikes a target and buries itself in the 
iron plate, the increased temperature of the united 
metallic masses is the result of the transfer of the 
motion of the ball, as a whole, to the molecules of 
which both ball and target consist ; and on the other 
hand, the piston of a steam-engine receives all its 
power from the molecules of steam which rebound 
from its surface. 

Sir WilUam Thompson used the word " atoms," 
meaning the units which chemists now distinguish by 

i6 



232 THE THEORY RESTS ON ANALOGY. 

the word ** molecules ; " but both atoms and mole- 
cules are of the same order of magnitude. 

Motion is thus transferred between large and small 
masses indifferently, as it would be transferred be- 
tween two elastic billiard-balls ; and indeed the v/ell- 
known laws of collision between elastic bodies were 
the basis of the analogy which led to the molecular 
theory. But in transferring our conceptions from 
ivory balls to molecules we are obliged to call on the 
imagination to take one of those extreme flights 
which all similar theories demand. Balls of ivory or 
steel, although made of the most elastic materials 
with which we are acquainted, would very soon come 
to rest in knocking about among each other ; but our 
molecules must be so perfectly elastic that though 
each one makes millions of collisions every second, 
yet throughout all time no moving power is lost. 

If we think only of their minuteness, the moving 
power of molecules may seem insignificant ; but the 
molecules are as numerous as they are small, and 
their aggregate moving power is enormous. When 
a quart of water is heated from the freezing to the 
boiling point, as in the familiar process of boiling a 
teakettle, an amount of moving power is imparted to 
the molecules of water which, if transferred to a 
pound cannon-ball, would impart to it an initial ve- 
locity of 4,715 feet a second. 

In a solid body the molecular motions are limited 
by the various forces which determine its structure, 
and are supposed to be restricted to a definite orbit. 
In a liquid the motion is less constrained, but is lim- 
ited by the boundaries of the liquid mass. In a gas, 



SUCCESS OF THE THEORY. 233 

however, the molecular motions are supposed to be 
entirely free, limited only by mutual collisions, or by 
the walls of the containing vessel. In both solids 
and liquids the relations are both so complex and 
obscure that the molecular theory has not been able 
to solve, except to a very limited extent, the difficult 
problems which they present; but with aeriform 
matter the theory has been far more successful, and 
gives a very satisfactory explanation of most of the 
observed phenomena. The tension or pressure ex- 
erted by a gas is the effect of molecular bombard- 
ment; and the well-known laws of Mariotte, of Charles, 
and of Avogadro, which define the condition of aeri- 
form matter have been shown to be necessary con- 
sequences of the molecular theory. 

Like the undulatory theory, the molecular theory 
has also led us to a knowledge of magnitudes which 
must ever evade our senses, and which almost defy 
our imagination. Thus we can calculate with great 
accuracy the average velocity of the molecular mo- 
tion in any gas under given conditions, — that in 
hydrogen gas at the freezing-point, for example, being 
6,099 feet in a second. And what is still more singu- 
lar, we can calculate the average number of collisions 
per second, as well as the average length of the mo- 
lecular path between two successive collisions, of 
course under definite conditions. In hydrogen gas, 
under the standard conditions of temperature and 
pressure, each molecule strikes against its fellows 
17,750 million times a second; and the average mo- 
lecular path is only 3 1 ten-m*illionths of an inch. This 
last seems incredibly small, but it is at least 136 



234 DIFFICULTIES OF CONCEPTION. 

times the average distance between two molecules ; 
and in an assembly of men such an allowance would 
be regarded as very liberal. 

These few data, which might be greatly multiplied, 
will show how definite are the conceptions which the 
molecular theory involves ; and my brief description 
will give some idea, although very imperfect, of the 
scope of the theory itself I can only add that in its 
relations to aeriform matter the theory has been de- 
veloped mathematically by such men as Rankine, 
Clausius, and Maxwell ; and that it gives a satisfac- 
tory account of the efficiency and mode of action of 
all thermo-motors, which, like the steam-engine, are 
such important factors in our civilized life. 

But while in that special field known as the " kin- 
etic theory of gases," the molecular theory is one of 
the best elaborated systems of modern science, it 
involves difficulties of conception fully as great as 
those we met in connection with the undulatory the- 
ory of light. Not only must we ascribe to the mole- 
cules a perfection of attributes, like perfect elasticity, 
which we only find in material bodies to a very 
limited degree, but also we must associate together 
attributes which from our experience seem to be in- 
compatible. We must, in a word, give up all our or- 
dinary prepossessions, and accept provisionally what 
seem to us monstrous hypotheses because they ex- 
plain facts and relations which would be otherwise 
isolated phenomena, and because they are parts of a 
system which as a whole is a good working theory. 

Having discussed similar difficulties of conception 
in the undulatory theory of light, it is unnecessary for 



CHEMICAL ASPECTS OF THE THEORY. 235 

me to dwell on the corresponding features in the sys- 
tem now before us. They obviously result from the 
same incompleteness of knowledge, and teach the 
same lessons already sufficiently enforced. Any one, 
however, who desires to study the details, will find 
them very clearly stated by J. B. Stallo, in his admir- 
able book on "The Concepts and Theories of Modern 
Physics," — a volume of the International Series to 
which I take great pleasure in referring. 

I wish next to ask your attention to the chemical 
side of the molecular theory; for it is in this direc- 
tion that it has run into the greatest extravagances ; 
and yet, singular as it may seem, it is just here that 
it has proved of the most value as a working theory. 
In addition to molecules, the chemist is obliged to 
distinguish a still smaller subdivision of matter, which 
he calls " atoms." The ultimate analysis of the physi- 
cist goes no further than molecules ; but the ultimate 
analysis of the chemist breaks up the molecules and 
gives us atoms. There must be as many kinds of 
molecules as there are distinct substances ; but only 
as many kinds of atoms as there are elementary sub- 
stances, some seventy at most. In a physical change 
in which the distinctions of substance remain unaltered 
the integrity of the molecules is preserved ; but in a 
chemical change, which necessarily involves a change 
of substance, the molecules are broken up, and the 
atoms regroup themselves to form the molecules of 
the resulting products. 

Thus when water is converted into steam, the mole- 
cules of water remain unchanged, and are only driven 
more widely apart ; but when under the action of an 



^36 THE CHEMICAL MOLECULE. 

electric current water yields oxygen and hydrogen 
gases, the molecules of water are broken up into 
atoms of oxygen and hydrogen, which regroup them- 
selves to form the molecules of these aeriform 
products. 

In fact the chemist regards the molecule in quite 
a different light from the physicist. To the latter, 
molecules are chiefly centres of force ; while to the 
chemist they are more or less complex structures on 
which depend the distinctions and relations of sub- 
stance. The qualities of substances are all referred 
to the molecules. The properties which distinguish 
water from alcohol, or sugar from salt, depend, not 
on the relations of any perceptible masses of these 
substances, but ultimately on the constitution of their 
molecules. Divide up a lump of sugar, and you may 
still distinguish the qualities of sugar in the smallest 
visible particles ; but the chemist declares such a sub- 
division could not be carried on indefinitely, even if 
our senses could follow it. We should soon come to 
the smallest possible mass of sugar, which on push- 
ing our subdivision further would break up into atoms 
of carbon, hydrogen, and oxygen, three well-known 
chemical elements. This smallest possible mass of a 
substance is the chemist's molecule; and hence his 
definition, — "the smallest mass of a substance which 
can exist by itself." 

The forces which bind together atoms into mole- 
cules we distinguish as chemical forces, while such 
as determine the aggregation of molecules to form 
material masses are said to be physical, although we 
have no sufficient reason for assuming that there is 



DISSOCIATION. 237 



any essential difference between the two ; and all such 
forces, whatever may be their nature, are overcome 
by heat. At the intensely high temperatures which 
rule at the sun or at the fixed stars, it is supposed 
that the elementary atoms are isolated and intermin- 
gled, if not still further resolved ; and as in the pro- 
cess of evolution of our system the planetary masses 
have cooled, it is held that the atoms have united to 
form the molecules of various substances, and that 
similar molecules have then aggregated to form defi- 
nite material products. When, now, on the surface of 
the earth we heat such materials to the highest tem- 
peratures we can command, the process of world- 
building is to a limited extent reversed, presenting 
us with a remarkable class of phenomena known as 
dissociation. But why in the process of evolution 
unlike atoms should unite by preference to form 
molecules, while in the further aggregation to form 
material products only, like molecules should asso- 
ciate together, remains an unexplained enigma. 

A confusion often arises from the use of the word 
" elementary" in connection with substances as well as 
with atoms. The atoms are the only true chemical 
elements. An elementary substance like oxygen gas, 
sulphur, or iron, is an aggregate of molecules like 
any other substances, and externally presents no 
characters by which it can be recognized as elemen- 
tary. But on analysis we find that its molecules are 
formed by the union of atoms of the same kind only, 
while the molecules of compound substances consist 
of atoms of different kinds. The molecules of oxygen 
gas, for example, are aggregates of atoms, as well as 



238 PHILOSOPHY OF CHEMISTRY. 

the molecules of water ; but while the first consist of 
oxygen atoms only, the second contain atoms of 
hydrogen united to the atoms of oxygen. 

Upon the distinction between atoms and molecules 
the philosophy of modern chemistry rests, and its 
symbolical language is based. Each one of the 
seventy chemical symbols stands for an atom. By 
grouping these symbols together, like letters to form 
a word, we represent the infinite possible varieties of 
molecules ; and then all chemical changes are repre- 
sented by an equation, writing the symbols of the 
substances concurring to produce the change in the 
first member, and the symbols of the substances 
resulting from the change in the second member. 
Such an equation declares that the process consists, 
as already said, in the breaking up of the so-called 
factors into atoms, and the regrouping of the result- 
ing atoms to form the molecules of new substances, 
the products. 

In the vapor of mercury immediately above the 
boiling-point, the atoms appear to be completely dis- 
sociated, so that this aeriform substance must be re- 
garded as a mass of isolated atoms ; but this is a very 
exceptional condition on the surface of the earth. In 
a few of the elementary gases or vapors, and in some 
of the simpler compounds, we are able to recognize 
— when the substances are aeriform — molecules con- 
sisting of only two or three atoms. But the molecules 
of most bodies are far more complex ; and although 
as the complexity increases, our confidence in our 
inferences diminishes, yet with a considerable degree 
of confidence we can say that the molecules of some 



MOLECULAR STRUCTURE. 239 

of the most familiar materials are aggregates of more 
than a hundred of these assumed ultimate elements 
of matter. 

It was formerly thought that the qualities and 
chemical relations of a substance depended on the 
nature of the elementary atoms of which its molecules 
consisted, and resulted from a blending of the quali- 
ties of the chemical elements in some mysterious 
way ; but we now recognize that the chemical prop- 
erties of substances depend in great measure, at least, 
on the manner in which the atoms are grouped in 
their molecules ; and the order in which the different 
atoms are grouped in the molecules of substances is 
not only a legitimate object of inquiry, but is a sub- 
ject which has nearly engrossed the attention of the 
chemists of the world for the past twenty-five years. 

It would be impracticable in this course of lectures 
to give any clear conception of the nature of the 
evidence on which our knowledge of the atomic 
structure of molecules is based, or of the course of 
reasoning by which the accepted conclusions have 
been established. The subject is abstruse, and could 
not be made intelligible without entering largely into 
the details of chemistry.^ In any modern work on 
organic chemistry, you can see our conceptions of 
the atomic structures of the molecules of various 
substances exhibited by placing the atomic symbols 
in definite relations to each other and connecting 
them by dashes supposed to represent the atomic 

1 I have endeavored to present the subject in a popular form 
in my " New Chemistry," and to that book I must refer any one 
who desires such information. 



240 



STRUCTURAL FORMULAE. 



bonds. Such graphic representations are called struc- 
tural formulae, and are supposed to show at least the 
order in which the several atoms are united in the 
molecule. A single example of a structural formula 
will suffice as an illustration : — 

H 
i 

O 

c c 



II 



H 



H 
C 

c 

I 

H 



H 



^k 



o c 

I II 

o c 



H 



Alizarine. 



To one who realizes what is thus represented, but 
who is not familiar with the evidence, or imbued 
with the spirit of the matter, it must seem incredible 
that these apparently fanciful groupings should be 
sober results of science ; and yet a reason can be 
given for the position of every symbol and of every 
dash, which — if the postulates are granted — must 
be admitted to be cogent. Moreover — what is the 
more remarkable fact — by following out the indica- 
tions of such structural formulae chemists have, suc- 
ceeded in preparing artificially a very large number 
of exceedingly complex compounds whose produc- 
tion under such circumstances could not but inspire 
the greatest confidence in the general correctness 
of the reasoning on which the structural formulae 
were based. Some of these products, like alizarine, 



CONVENTIONAL SYMBOLS. 24 1 

the coloring- matter of madder- root, — now prepared 
artificially from anthracene, one of the constitu- 
ents of coal tar, — have such great commercial im- 
portance that these theoretical investigations have 
completely revolutionized large branches of human 
industry. Indeed if certainty of prediction is to be 
regarded as the test of validity, there is not one of 
the great systems of science, excepting the the- 
ory of gravitation, which has so completely vindi- 
cated its legitimacy as has this molecular theory of 
chemistry. 

But although our structural formulae have this 
wonderful power of prediction, and are therefore of 
the highest value as a system of science, yet no 
philosophical chemist thinks of regarding them as 
more than conventional symbols of relations which 
are at present incomprehensible. I would urge this 
point with special emphasis; because, although the 
same feature appears, as I have shown, in connection 
both with the theory of gravitation and with the un- 
dulatory theory of light, it has been said that the 
difficulties of conception, which an inherent gravitat- 
ing force or an adamantine ether present are of no 
weight in view of the so general accordance of these 
theories with observed facts. In the present case no 
such claim can for a moment be maintained. All the 
conceptions are obviously conventional ; and yet we 
have the same wonderful gift of prophecy. Is not 
the lesson plain? Man must work under Hmitations; 
he must often be content with the shadow instead of 
the substance of realities; but he may with confi- 
dence follow his earth-born systems of philosophy, if 



242 THEORY OF ORGANIC DEVELOPMENT. 

only they are grounded on experience and estab- 
lished in loyalty to truth. 

And if this course of conduct be safe and legiti- 
mate in one realm of thought it certainly must be 
equally so in every other. Spiritual experience can 
be no exception to the general principle. 

" Finding, following, keeping, struggling, 
Is He sure to bless ? 
Saints, apostles, prophets, martyrs 
Answer, ' Yes.' " 

Of the four great dominant systems in modern 
science to which I referred at the opening of this 
lecture I have as yet spoken of but three. The fourth 
during the last twenty-five years has attracted more 
attention than all the rest combined, and is insepara- 
bly associated with the name of that chief of natural- 
ists, Charles Darwin. All these systems have been in 
their turn the subject of controversy ; and too often 
the introduction of irrelevant theological issues has 
added acrimony to the debate. I say irrelevant be- 
cause, if the position I have taken in regard to the 
relations of scientific systems to actual knowledge be 
correct, there can be no real issue between theology 
and the theories of science, — anymore than between 
theology and the theory of music. In my view of 
the subject it is as useless to seek for theological an- 
tagonism in Darwinism as it would be to look for it 
in the Calculus. 

In regard to the other systems, whatever differ- 
ences of opinion may remain, all feeling about the 
matter has long since disappeared ; but in regard to 
Darwinism, while the blaze of theological protest with 



POSTULATES OF DARWINISM. 243 

which the theory was first received has died down, 
the embers of the excitement still remain ; and it is 
more difficult to discuss the subject dispassionately. 
In another place I have before strongly urged the 
irrelevancy of theological issues on this question; 
and I will only add here a few remarks, which may 
be deemed pertinent because showing how the subject 
is viewed by a student familiar with the bearings and 
use of theories in a very different department of 
science. Further than this I do not feel that it is 
within my province to discuss the subject; for my 
special studies have been limited to a very different 
field ; and I have not that detailed knowledge which 
alone would entitle me to express an authoritative 
opinion on the merits of the system. 

The theory of Darwin rests on three distinct postu- 
lates. The first is that the existing species of plants 
and animals are not independent creations, but the 
results of a gradual evolution from earlier forms. 
The second is that while in the provisions of nature 
for the propagation of all living beings there is evi- 
dently a strong striving for the conservation of types, 
there is also a manifest tendency to variation, which 
although barely perceptible in single steps may go 
on increasing in successive generations to an unlim- 
ited extent. The third is that in the struggle for 
existence those variations are preserved which are 
best adapted to the environment, and which therefore 
protect the individuals possessing them in the midst 
of the terrible mortality which the struggle for exist- 
ence entails. 

However many facts or considerations may be 



244 ANTIQUITY OF MAN. 

urged in their support, there is not one of these 
propositions which has been demonstrated beyond 
reasonable doubt ; so that this theory, Hke the other 
great theories of science, rests on hypotheses, and 
must be judged as a scientific system by the com- 
pleteness with which it explains the phenomena of 
nature. 

In regard to the first proposition it seems strange 
that with all the attention which has been directed to 
the point during the last twenty-five years the fact of 
a transition between two well-marked species has not 
yet been established conclusively. For, admitting 
all that has been said in regard to the slowness of 
the transition, or the imperfection of the geological 
record, yet considering the extent of the field that 
has been surveyed, it seems very strange that niore 
of the missing links have not been found. We can 
point with great precision to definite geological hori- 
zons — to use a now familiar technical term — on 
which certain species of well-marked types appeared 
on earth; and certainly, on the hypothesis we are 
considering, it is strange that we can in no case point 
unhesitatingly to other species in lower strata from 
which they descended, on the evidence of an un- 
broken series of the intermediate forms between 
the two. 

Take the case in which we are the most interested, 
that of our own race. Assume all that is claimed 
in regard to the antiquity of man. Still, there is a 
definite horizon of the tertiary epoch below which 
man is not, but above which his remains are found 
in ever increasing abundance, with all the features 



GROWTH THE ORDER OF NATURE. 245 

of man and his works as strongly marked as they 
are to-day. Skeletons of these primeval men, and 
their belongings, are to be seen in our ethnological 
museums; and there are no greater differences of 
structure between them and ourselves than between 
the different races which inhabit the earth at the 
present day. But if man be descended from " an 
anthropoid animal of arboreal habits," it is passing 
strange that so far as any direct evidence goes, he 
should have appeared on the earth thus suddenly, 
and that we can find no traces of his progenitors 
either of the first, second, third, or of any other 
generation. 

Nevertheless, the hypothesis of a gradual genesis 
of organic types seems to me not only reasonable 
in itself, but also in harmony with what we know of 
nature's workings. Growth, and not spasmodic ef- 
fort, is the usual order of the divine government 
both in the material and in the spiritual world ; and, 
reasoning from analogy, it is the method by which 
we should expect a new race of plants or animals 
would be introduced into the world. Indeed, from a 
scientific point of view any other mode is wholly un- 
thinkable. Conceive of an elephant suddenly appear- 
ing in a tropical jungle, like a jack in a box, without 
any antecedents except a fiat; and see if the thought 
does not put to confusion every dictate of your expe- 
rience, and every principle of your intelligence. You 
will then clearly see that if by mortifying reason the 
doctrine of independent creations can be accepted 
as a wonder, it cannot possibly be reconciled with 
the rest of your knowledge. Attempt further to 



246 QUESTION OF INTERPRETATION. 

realize in imagination the genesis of the first man. 
Was he suddenly created in his full development 
and strength, prepared to subdue nature? or did he 
come into the world as an infant, as have come 
all of his race since, — even the Saviour of the 
world ? 

Do not deem such questions irreverent. They are 
asked in that spirit of truth and soberness which 
sanctifies any inquiry. They ought not to be further 
pushed in this place ; but the suggestions they make, 
if followed out in your own reflections, will bring you 
to the point of view from which a naturalist is com- 
pelled to look at the question of the origin of spe- 
cies. Roman mythology provided the heaven-born 
founders of their state with a foster-mother ; and it 
is a similar necessity of thought which has led to 
what is usually regarded as the most objectionable 
feature of Darwinism. And apart from the au- 
thority of any undoubted declaration to the con- 
trary, why should we be shocked by the hypothesis 
here involved? 

On the other hand, it may be said. You admit that 
any prodigy must be accepted in science on ade- 
quate evidence ; why not then receive the plain doc- 
trine of independent creations taught by the Hebrew 
Scriptures? To this the Christian naturalist replies 
that all such inferences from the Scriptures must be 
to a very great extent questions of interpretation; 
and that in this case, as in so many instances before, 
the interpretation will be reconciled with the facts as 
soon as the truth plainly appears. And in the sec- 
ond place, he will add that while in science no won- 



POSSIBILITY OF INTERFERENCE, 247 

der is so great that it may not be realized, so also 
no marvel is so sacred that it may not be reverently 
investigated ; and that, whatever the event, the show- 
ing forth of the truth can only redound to the glory 
of God. Again, he may urge that this is a question 
between the interpretation of Nature on one side and 
of Scripture on the other, and that it ought not to 
be prejudged by assuming the infallibility of our ren- 
dering of either of these two co-ordinate authorities. 

Moreover, this is not a question of creative power 
nor of Divine Providence. After all has been granted 
that any one can claim in regard to the constancy of 
the laws which we fully understand, there is, as has 
been plainly shown, abundant room left for interfer- 
ence ; and it is more consistent with our conceptions 
of the Divine method to suppose that God works by 
introducing new conditions into old chains of causa- 
tion than by spasmodic acts of creation, which must 
inevitably confuse and confound the intelligences 
he holds so dear. That such interference has taken 
place, it seems to me that the transition from a geo- 
logical to an archaeological museum as plainly shows 
as any record can whose meaning has been left to 
human interpretation. And when with every Yule- 
tide the Christ Child becomes the emblem of all 
that is lovely, pure, and holy, why should we be 
alarmed at the supposition that as the Child of 
Mary ** grew and waxed strong in spirit " so m the 
beauty of innocence, human intelligence at first slowly 
awakened to the wonders of this earth? 

In regard to the second postulate on which Dar- 
winism rests, we must admit that this also is to a great 
17 



248 EVIDENCE INCONCLUSIVE. 

extent in harmony with well-established facts. No 
one can study the aspects and characters of a family 
of children without being struck with the undoubted 
truth that while minute details of features both of 
body and mind are wonderfully preserved, striking 
variations from the parent type are equally conspic- 
uous. The same is seen to be even more markedly 
true of the lower animals when we watch them as 
closely ; and when we think of it, the wonder is that 
the variations are not greater than they are. 

There is nothing in our actual knowledge of na- 
ture which makes it any less strange that an acorn 
should always grow into an oak than that a race 
of monkeys after unnumbered generations should 
assimilate to men; and we know of no reason what- 
ever why, with an equal experience, one change 
should not appear as natural as the other. Indeed 
I feel confident that, with all our knowledge of em- 
bryology, any one who reflects on the mysteries 
which the beginnings of life both in plants and ani- 
mals present, will conclude that it is a far more re- 
markable fact that every creature should produce of 
its kind, than that occasional variations should occur. 
Nor is there any reason why we should be surprised 
to learn that in successive generations the variations 
should become cumulative, and lead to such a de- 
parture from the original type as to amount to a 
difference of species. 

As before said, however, it is strange that the 
evidence of such a transition is so limited and incon- 
clusive ; and moreover, as was so strongly urged by 
the late Professor Agassiz, that the variations pro- 



NATURAL SELECTION. 249 

duced by domestication — which have been so care- 
fully studied by the propagators of plants, and the 
breeders of stock — all tend to revert to the original 
wild condition. 

Coming lastly to the third postulate, we find in this 
also a general principle which appears to a student 
of nature highly plausible. The struggle for life 
among the lower animals is a condition, the violence 
and destructiveness of which is wholly unappreciated 
except by those who have made a special study of 
the subject. The survivors of this internecine war- 
fare who finish their allotted span of life are fre- 
quently not one in a hundred, often not one in a 
thousand. Tennyson quite understates the condition 
when he speaks of — 

" finding that of fifty seeds 
She often brings but one to bear." 

Even in our own race the mortality is frightful to con- 
template, — as Malthus has so vividly depicted it in 
his great work on population. Professor Wallace, who, 
independently of Darwin, and almost at the same 
time, originated the doctrine of natural selection, has 
distinctly said that it was the work of Malthus which 
gave him the key to the problem; and it is well 
known that Darwin himself was also strongly influ- 
enced by the facts so powerfully set forth in that re- 
markable book. I only repeat what some of you must 
have heard from Professor Wallace's own lips when 
I say that until one realizes the prodigal destruc- 
tiveness of nature it is impossible to appreciate the 
strength of the doctrine of natural selection. Wallace 
also has stated that the generalization came to him as 



250 ADAPTATION TO THE ENVIRONMENT. 

a sudden thought, — when, overpowered with what 
he was constantly witnessing in the East Indies, he 
stopped to reflect on the necessary issues of such 
fearful mortality. The "survival of the fittest" was to 
him a fact of observation ; and by the indiscriminate 
slaughter of all others, a selection was seen to be 
made of those creatures whose features best fitted 
them to cope with their surroundings. The conclu- 
sion was that any accidental variation in color or 
form which better equipped the animal for the in- 
evitable fight must be preserved ; and that thus came 
the gradual adaptation to the environment in which 
natural selection consists. 

All this is plausible, and to most naturalists con- 
clusive ; and that the struggle for existence must 
tend to perpetuate varieties seems to be beyond 
question. It still remains, however, to determine 
how far variations thus caused can proceed; and 
whether they can ever lead to fundamental differ- 
ences of type. The assumption that all forms of 
plants and animals may have been thus produced 
from a few germs is as yet an hypothesis, to be 
judged, like any other hypothesis, by the extent to 
which it explains and correlates facts. Let it not be 
prejudged on any theory of Divine government, or 
on the basis of any speculative views about the na- 
ture of causation ; for, were the hypothesis estab- 
lished without reservation, — a most improbable event, 
judging from the past history of science, — the new 
truth would only serve to enlarge our views of the 
mode of the Divine government ; and there is abun- 
dant room for causation left. 



VALUE OF THE THEORY. 25 I 

Assume that the variations preserved by natural 
selection are all accidental, a point on which natu- 
raHsts greatly differ, still what is the result? An 
adaptation to the environment. According to the 
theory, then, the conditions of the environment are 
a determining cause ; and unless we believe that all 
nature was the result of a fortuitous concourse of 
atoms, we can find in these conditions abundant 
opportunities where intelligent causation can act. 
And the thought which the terrible facts implied in 
our theory force on the mind, are they not wholly in 
harmony with what we believe in regard to the Di- 
vine plan? Everywhere in this world are not benefi- 
cent results worked out through suffering? And to 
the lines of the English poet which I have just 
quoted, must I not add the anti-strophe from pre- 
ceding stanzas? — 

" O yet we trust, that somehow good 
Will be the- final goal of ill, 
To pangs of nature, sins of will, 
Defects of doubt and taints of blood. 

" That nothing walks with aimless feet, 
That not one life shall be destroyed, 
Or cast as rubbish to the void, 
When God hath made the pile complete." 

Finally, looking at the Darwinian theory of devel- 
opment for a few moments as a whole, I would re- 
mark that it has not the completeness of the other 
dominant theories of science ; and that the modes of 
action which it predicates have not been worked out. 
It is a doctrine rather than a complete system of 
science. Nevertheless, it is a doctrine which exerts 



252 ORGANIC TYPES. 



very great power. It owes its influence over natural 
history students solely to the wonderful effect it has 
exerted in directing and stimulating investigation, as 
well as to its capability of exhibiting order and har- 
mony among many classes of facts whose relations 
before were very obscure, if not wholly unrecogniz- 
able. Its influence on the religious thought of the 
student will depend very greatly on the manner in 
which its philosophy is presented by his religious 
teachers; and I therefore greatly deprecate hasty 
judgment or indiscriminating censure. Remember 
that, though not proven, it is a useful and admirable 
theory of science, and can be made an influence for 
good instead of for evil, if only set forth in the right 
light, and candidly accepted for its great worth 
within its proper sphere and just limitations. Set 
at naught all questions of intelligent or unintelligent 
causation as irrelevant, on which scientific theories 
have no bearing. The character of the First Cause 
cannot be judged from the mode of action of any 
secondary agencies. One mode of action is as mys- 
terious as another, so far as any relations to a First 
Cause are concerned. The intelligence of the First 
Cause can only be judged from the result. Each 
man has grown from a germ ; and we do not disown 
creative power when, for the sake of a consistent 
system, we assume that the species grew as well. 

I myself deprecate the present domination of the 
Darwinian theory, not on account of what it is in 
itself, but because it has for a time thrust to one side, 
and cast into the shade, the doctrine of ** organic 
types " so ably and so forcibly advocated by my late 



ORGANIC TYPES. 253 



teacher and colleague, Professor Louis Agassiz, and 
which I believe to be the more valuable system of 
the two, at least in one important respect. 

The conception that each of the four great fam- 
ilies of the animal kingdom is a definite plan, a spe- 
cific design, a creative thought, worked out in infinite 
variety, and adapted, possibly through the principles 
of natural selection, to varying conditions of soil or 
climate, is to me a far grander and more compre- 
hensive doctrine than the one which now so exclu- 
sively prevails. * The idea that types of structure are 
forms of thought is moreover an hypothesis which 
has very great intellectual reach and educational 
value ; and for this great virtue of the older theory^ 
Darwinism offers no sufficient substitute. When now 
we consider that the educational power of a scientific 
system is its chief element of strength, we cannot but 
regret that the present generation will lose much of 
the charm which the grand conceptions of Cuvier and 
Agassiz imparted to the study of natural history. 

It is to be expected that a theory at once so origi- 
nal and so fruitful of suggestions as Darwinism 
should for a season control thought, and engross 
attention. But time may be trusted to place all 
human systems in their true relations; and I feel 
confident that the doctrine of organic types will 
before long exert its just influence. The new and 
the older conceptions are not mutually exclusive. 
Whatever is true in each will survive; whatever is 
false will be forgotten; and out of the limited hy- 
potheses of to-day will grow the larger views of 
coming generations. 



254 THE DOGMATIST. 



Having discussed the more characteristic features 
of the dominant systems of science, I will next add a 
few words in regard to the attitude of scientific schol- 
ars towards these systems, as there are marked differ- 
ences in this respect which strikingly illustrate a 
point I desire to emphasize. 

In the first place, then, we distinguish a very large 
and efficient class of scientific scholars who are wholly 
wedded to the system of science by which their stud- 
ies are directed. They are men to whom the system 
gives strength and motive, and their whole intellectual 
life has been moulded by their guide. No wonder 
that they value the system, for it has made them what 
they are, and without it they would be to a great 
extent helpless. They are not men who originate 
systems or strike out new paths of discovery, but 
they are men who with a well-defined aim work zeal- 
ously and efficiently. The system has opened to 
them new fields of investigation from which they 
have reaped an abundant harvest. They have thus 
extended the boundaries of knowledge, and are in 
consequence deservedly highly honored by their fel- 
low-men. It is impossible that a system through 
which they have realized such great results, should 
be at fault or even have a blemish. Imperfections, 
which to other men appear glaring, they refer to 
errors of observation ; inconsistencies are overlooked 
or ingeniously explained away, and mere philosophi- 
cal objections are laughed to scorn. By such men 
the obvious symbolism of the system often comes to 
be regarded as a likeness of real things; and they 
dwell with equal emphasis on the essentials and the 



THE DOGMATIST. 255 

non-essentials of these arbitrary signs. Sometimes 
they even parade the extravagances of the system in 
order to testify more conspicuously their allegiance 
to their leader. 

Such men are apt to be dogmatic, and to demand 
conformity to their well-grounded opinion as well as 
deference to their long experience. They do not 
readily brook dissent, especially from younger men ; 
and when they have the power, they are sometimes 
tyrannical. The tyranny of a system is often as cruel 
as the tyranny of a despot, and may be exercised 
with complacency and self-respect by the " mens sibi 
conscia recti," who thinks he holds the keys of knowl- 
edge. We must not overlook what is often noble 
and worthy in these men. They are actuated by the 
power of conviction which a successful system in- 
spires, and the intolerance of conviction is often asso- 
ciated with all that is pure, lovely, and of good report. 
There is a still nobler charity, which never faileth ; 
but scholars are not always saints, and ostracism is 
a form of persecution which requires no sanguinary 
edicts. The noblest martyrs of science are not those 
who have braved great dangers and succumbed only 
before the unattainable ; but rather those who have 
suffered even unto death, in consequence of deprecia- 
tion, deprivation, and neglect. I have known of such, 
and among them the founders of one of the now 
dominant systems of science. Boycotting did not 
originate in Ireland; and among men of learning 
supercilious sneers may cause more suffering than 
blackballing. Scientific societies are probably no 
worse than other associations of men ; but they have 



256 THE THEORIST. 



often been subservient to the intolerance of doctrine, 
and the domination of system. 

A very much smaller class of scientific scholars 
display a habit of mind the very reverse of that I 
have just described. These men are superior to 
systems, of which, however, they speak with respect 
and condescension as the necessities of weak minds. 
They boast of their freedom from prejudice, and of 
their eclecticism in thought. They magnify incon- 
sistencies of doctrine, or incompleteness of evidence. 
They expose the extravagances of the assumptions, 
or the unsoundness of the philosophy on which the 
dominant system is based. They are apt to be severe 
critics, and not to make due allowance for the limita- 
tions of methods or the necessary imperfections of 
all material results. They deal with negations rather 
than with affirmations, and see blemishes more readily 
than beauties. They are largely tolerant in theory, 
but they esteem the freedom of dissent more than 
the freedom of conviction. Such persons are usually 
prone to speculation, and are often fruitful in in- 
genious suggestions ; but they have seldom the incli- 
nation or the patience for the tedious experimental 
work required to verify their hypotheses. They are, 
as a rule, highly imaginative, and their fancy paints 
with glowing colors every subject which they study ; 
but their deductions are not always trustworthy, and 
their generalizations are often more subtile than pro- 
found. They are sanguine students, and their enthu- 
siasm invests their teaching with a peculiar charm ; 
but their zeal is not always tempered by prudence, 
and they are apt to be better expositors of what is 



THE POSITIVIST. 257 



known than investigators of what is unknown. Men 
of this temperament are not unfrequently truly hberal- 
minded, capable of large views, and fitted to be 
leaders ; and have exerted more influence on the ad- 
vancement of knowledge than many a harder student 
or deeper thinker. 

Then there is another class of scientific students 
quite different from either of the two types we have 
sketched, and one which the specialism of our day is 
tending very greatly to multiply. Among this class 
are to be found many of the exact anatomists in 
natural history, the accurate analysts in chemistry, 
the untiring observers in astronomy, men who do 
much of the hard work of science, and on whose un- 
swerving truthfulness and scrupulous exactness entire 
confidence can be placed. Minds which are occupied 
with minute details, which delight in delicate distinc- 
tions, and find pleasure in pushing observations to 
the extreme limit of accuracy, are apt to overlook 
the broader relations of truth, and value only definite 
results ; and it is among such students that the posi- 
tive philosophy finds most of its disciples. The class 
of men to whom we refer includes not only those 
who actually avow the doctrines of positivism, but 
also those who cherish a similar habit of mind, — 
men who worship facts and have little faith in ideals ; 
men who never had any visions themselves, and there- 
fore regard all visions as hallucinations ; men to whom 
the material is the only reality, and the spiritual a 
dream. Such men often condemn as idle specula- 
tions the very hypotheses by which their own studies 
have been guided, and despise the theories which 



258 THE TRUE SPIRIT. 

alone give significance to the facts that have cost 
them so dearly. These are worthy men and sincerely 
devoted to the truth ; but their range is narrow, and 
their prospect restricted. They have always dwelt in 
a narrow valley amid pleasant pastures and beside 
still waters. They have never ascended unto the hills 
around them; they never have been awed by the 
mountain torrent; they never have been oppressed 
by the mountain gloom ; they never have been glad- 
dened by the mountain vision. 

These are not ideal sketches which I have at- 
tempted to draw. They are lineaments of real men, 
whose biographies you may read in the history of 
science ; whom you may meet to-day in every large 
society of scholars ; whom you all must have known. 
Such characters are not the products of scientific 
study only. They are equally marked in every de- 
partment of learning. In politics they are conserva- 
tists, liberals, or bureaucratists. In philosophy they 
become realists, nominahsts, or positivists. In the- 
ology they are classed as low, broad, or high church ; 
and they are recognized as conventionalists, impres- 
sionists, or preraphaehtes in art. We must seek for 
the origin of such distinctions far down in the varying 
dispositions of the human mind and in the influences 
of education. However much they may be exagger- 
ated by passion, or misguided by evil counsel, these 
traits of character are all good in themselves ; and 
when blended in due proportion, they make the Solons, 
the Washingtons, the Shakspeares, the Miltons, the 
Newtons, the Faradays, of history. But so rarely are 
such qualities of mind combined that we often regard 



THE TRUE SPIRIT. 259 

them as incompatible. You do not expect to find in 
a poet that attention to minute details which marks 
the man of affairs ; nor in a wise counsellor the im- 
agination of an artist; yet in the great pioneers of 
science such opposite faculties have been united in a 
most remarkable degree. They have been men of 
ideals, but men whose vivid imaginations were regu- 
lated by education, and chastened by wisdom. They 
have been men of courage and perseverance, who fol- 
lowed out their convictions through every discour- 
agement. They have been men of entire truthfulness 
who have never hesitated to submit their doctrines to 
the test of crucial experiments and to abide by the 
issue. They have been men of the most scrupulous 
conscientiousness in attention to minute details, re- 
garding themselves as responsible to the Giver of all 
truth for accuracy in every observation, and for ex- 
actness in every statement. Finally, they have been 
men of modesty and of reserve in judgment, realizing, 
as no other men ever have, how boundless is truth ; 
how limited knowledge ; how intricate the problem 
of nature ; how weak in comparison the intellect of 
man. 



260 DICTATES OF EXPERIENCE. 



LECTURE IX. 

PREDOMINANT PRINCIPLES OF SCIENTIFIC 
THOUGHT. 

WE have already in the preceding lectures dis- 
cussed at some length the validity and char-, 
acter both of the inductive and of the deductive forms 
of scientific reasoning ; we have also studied the au- 
thority and relations of the laws of nature, as well 
as the warrant and use of scientific systems ; and in 
order to complete my survey of the general methods 
of science, I propose lastly to consider very briefly 
certain general principles by which students of nature 
have been greatly guided, and which, therefore, have 
exerted a marked influence on the progress of knowl- 
edge. As I have already said, the mental process of 
induction is subject to no known laws that can be 
accurately defined. It is a product of genius whose 
antecedents we can rarely trace, and whose conditions 
we can seldom analyze. Nevertheless, even genius is 
guided by experience ; and there are two dictates of 
experience so wide in their application, and so gen- 
erally trustworthy, that they claim our notice in this 
connection. I refer to the principles of analogy 
and of continuity, which although often found deceit- 
ful guides, yet when followed with caution and judg- 



ANALOGY. 261 



ment very seldom lead astray. Other suggestions 
of experience, like the principles of least waste, of 
the sufficient reason, of successive approach, of adap- 
tation, and of intelligent plan, have been found at 
times of great value in the study of science; but 
they are not principles so generally accepted as 
those first named, and are more restricted in their 
appHcation. 

There can be no question that the suggestions of 
analogy have led to more discoveries in science than 
all other influences combined. 

If the force of the earth's gravitation is not sensibly 
diminished at the summits of the highest mountains, 
why may it not reach to the moon? Since the phe- 
nomena of light resemble in so many respects those 
of sound, why may they not be, like these, the effects 
of wave-motion? If there be in masses of matter an 
internal molecular motion which produces thermal 
changes, why should not these motions obey the well- 
known laws which govern the motions of the masses 
themselves? If, as Malthus has shown, the struggle 
for existence has exerted such a marked influence on 
the history of the human race, why should it not 
produce far deeper and more lasting efl'ects among 
the lower animals, where the struggle is vastly more 
intense? Thus it is through analogy that men have 
been led to each of the great systems of science 
now dominant in the intellectual world. So also 
in unnumbered other instances analogy has given 
the suggestion which observation or experiment has 
verified. 

The astronomer noticed through the telescope 



262 DECOMPOSITION OF THE ALKALIES. 

patches of dazzling whiteness around the poles of 
Mars; and since this planet moves around the sun 
under relations similar to those of the earth, he in- 
ferred that the greater brilliancy was caused by the 
reflection of light from snow-caps like those which 
render the earth's poles so inaccessible ; and when on 
watching the planet's disk from year to year, he ob- 
served that these patches alternately increased and 
diminished with the changing Martial seasons, he felt 
assured that this suggestion of analogy was correct. 

Down to the beginning of this century the so-called 
earths and alkalies, such as alumina, magnesia, lime, 
soda, and potash, had been regarded as elementary 
substances ; but towards the close of the last century 
Lavoisier had shown that several materials closely 
resembling the earths, such as iron-rust, litharge, 
and tinstone, were compounds of metals with the 
then newly discovered oxygen gas. Analogy at 
once suggested that the earths and alkalies must also 
contain metals united to oxygen ; but although the 
analogy inspired a confident behef in this inference, 
the chemists at the time did not succeed in decom- 
posing the compounds, because the means at their 
command were inadequate. But the discoveries of 
Galvani and Volta gave the world a new agent in 
voltaic electricity, which by the decomposition of 
water proved to be a reducing force of wonderful 
power; and the first moment he could command a 
voltaic battery of suflficient strength Sir Humphry 
Davy applied the new force to the alkahes, when out 
at once the metals flowed. 

In 1812 iodine was discovered by Courtois in the 



SPECIFIC FOR GOITRE. 263 

crude soda-salt called kelp, which is prepared by 
burning wrack, and is simply the ashes of this sea- 
weed. For a long time previously burnt sponge had 
been used as a remedy in cases of goitre, which in 
the mountainous regions of Switzerland produces 
such wide-spread and distressing results. As sponge* 
in its habitat and relations resembles sea-weed, anal- 
ogy suggested that the burnt sponge might contain 
a minute amount of iodine, and that its efficacy 
might be due to this new elementary substance ; and 
in 1820 Dr. Coindet, a physician of Geneva, aided by 
the young chemist Dumas, succeeded not only in 
proving the presence of iodine in the sponge, but in 
replacing a nauseous dose by preparations of iodine 
which have proved almost a specific for the terrible 
disease. 

Such examples might be multipHed indefinitely; 
but we have only time for one other, which is, how- 
ever, very striking. As we have before said, the ele- 
mentary rays of a beam of light must be regarded as 
moving in a definite plane; and a beam all whose 
rays are moving in the same plane is said to be po- 
larized. By optical means we can readily determine 
the position of this plane, which we call **the plane 
of vibration," sometimes also *' the plane of polariza- 
tion." When a polarized beam of light passes through 
a plate of quartz in the direction of the axis of the 
well-known hexagonal crystals of this mineral the 
plane of polarization suffers a rotation, to an extent 
depending on the thickness of the plate. Now on 
some of the hexagonal crystals .in which quartz crys- 
tallizes there are to be found certain small planes, 
18 



264 MAGNETIC STRAIN. 

called " plagihedral," which are distributed after a 
helioidal, or spiral-like, type of symmetry; and ac- 
cording as the spiral ascends to the right or to the 
left, the plane of polarization is rotated to one side or 
to the other. Remember also that the effects of 
crystals on light are referred by the undulatory 
theory to their unequal elasticity in different direc- 
tions, and that similar effects can be obtained with 
homogeneous glass by subjecting this transparent 
material to unequal strains, and thus developing un- 
equal elasticity in different directions ; add to all this 
the further fact that when a current of electricity flows 
through a spiral of copper wire wound round a bar 
of iron, and renders it magnetic, a screw-like strain is 
developed in the bar, — and you will then have the 
basis from which Sir John Herschel, to whom these 
facts and theories were very familiar, inferred by 
analogy that if glass or other transparent material 
could be subjected to a similar magnetic strain, we 
might obtain under such conditions the same effect 
of rotating the plane of polarization which is so 
markedly exhibited by quartz; and further, that 
possibly such a strain might be developed by a 
powerful electro-magnet. Herschel himself never 
verified this suggestion of analogy; but the effect 
was subsequently realized in a most striking manner 
by Faraday. 

The validity of analogical reasoning unquestionably 
depends on the harmonies of nature. Since the uni- 
verse has been made throughout on one plan, and, 
however varied the details, the same general patterns 
reappear in all its parts, both great and small, we can 



VALIDITY OF ANALOGICAL REASONING. 265 

safely infer from our very limited experience in a 
narrow field what are the conditions and relations in 
remote and inaccessible provinces which we can 
never directly explore with our senses. Hence it is 
that we can infer that molecules and atoms obey the 
same laws of motion as suns and planets. It is 
wholly conceivable that the microcosmos should 
have been planned on a system entirely different 
from that of the macrocosmos; but apparently the 
very reverse is the truth; and a theory, which as- 
sumes that within the masses of material bodies the 
motions of suns and systems are reproduced on a 
scale so minute as to task our power of imagination 
to grasp the conception, is found to be in complete 
accordance with all the facts which can be observed. 
Moreover, whenever we have been able to obtain evi- 
dence we have found our reliance on the unity of 
nature fully justified. 

Within a comparatively few years our confidence 
in this regard has been very greatly strengthened by 
the revelations of the spectroscope. If our globe 
was once thrown off from the sun we might expect 
that it would be a chip of the old block ; but we can 
conceive of no necessity which requires that the ma- 
terials of the fixed stars should be like that of our 
earth. Still, the spectroscope tells us that in those 
immensely distant bodies the same elementary sub- 
stances are glowing with which we are so familiar in 
our laboratories. And if anywhere in the depths of 
space there revolves around one of those centres of 
energy a globe which has been reduced to the cli- 
matic conditions of our earth, we can infer with a 



266 VALIDITY OF ANALOGICAL REASONING. 

confidence which approaches certainty that its rocks 
contain the same minerals, and that its plants and 
animals are fashioned after the same patterns with 
which we are so familiar ; and, if it has also become 
the abode of intelligent beings, that they have been 
discussing the same great problems which have per- 
plexed man. 

It is solely the unity and harmony of nature which 
renders analogical reasoning valid. To this harmony 
our own being answers, and it is only because we are 
in unison with nature that we are able to interpret her 
methods. Were our minds not in harmony with our 
surroundings, or those surroundings not in harmony 
with the rest of creation, our intelligences would have 
been confounded, and all nature would have been to 
us a sealed book. 

Man cannot conceive in a concrete form of any- 
thing he has not previously received through the 
senses. No hypothesis can be so much as framed 
in the mind which has not some semblance in pre- 
vious experience ; and as through our senses we have 
direct cognizance only of material things, we cannot 
picture to ourselves any existences without associ- 
ating with them some of the qualities of matter. The 
most we can do is to alter the combinations of our 
experience, or to change in degree the qualities we 
have actually observed. This is all we have done in 
forming the most subtile conception man has ever 
grasped, — that of the luminiferous ether. We are 
familiar with elasticity, and we can predicate an 
elasticity a million or a billion times greater than 
any that is known to us. We know what density 



FAILURES OF ANALOGY. 267 

is, and we can at least in words describe a material 
less dense than any known substance in a similar 
extreme degree, and then in imagination combine 
these extravagances. But what we reach is a con- 
dition of matter, and all our calculations in regard 
to it are based on its likeness to matter. We can, in 
imagination, vary the known qualities of matter to 
an unlimited degree. We can combine these quali- 
ties in other than the accustomed relations. But, 
however much we may think or talk about other 
states of existence, we cannot actually picture to 
ourselves any existence or mode of action of which 
experience has not given us some semblance. Thus 
all our science — that is, our knowledge of things — 
rests on experience, and never could have been built 
up had not the unknown been of a piece with the 
known. 

But while analogy is thus the guiding rule of sci- 
entific thought, it is a rule which cannot be blindly 
followed. The suggestions of analogy have often 
proved delusive, — either because the resemblances 
on which we counted were superficial and not real, 
or because our scientific methods and appliances 
were inadequate to establish the relations we sus- 
pected. The history of science is full of examples 
of misdirected efforts whose failure is to be attri- 
buted to one or the other of these causes. Two 
marked instances will serve as illustrations. 

After the elder Herschel with his large telescope 
had distinguished in several of the nebulae points of 
light, and later Lord Rosse with a much larger re- 
flector had resolved still more of these distant star- 



268 FAILURES OF ANALOGY. 

clusters, it was inferred by astronomers that all the 
nebulae were groups of stars, whose resolution was 
only a question of telescopic power. But since the 
application of the spectroscope to the problem it 
has been found that there is a very large class of 
these objects which are masses of luminous vapors; 
and it is evident that the astronomers were at first 
deceived by a superficial resemblance. 

Faraday, after he had investigated with such con- 
summate skill the relations of electricity to mag- 
netism, conceived that similar relations must exist 
between these modes of energy and gravitation ; and 
devoted a great deal of labor and thought to the in- 
vestigation of the subject. He made several series 
of laborious experiments in the clock-tower of the 
Houses of Parliament and elsewhere, but with abso- 
lutely no results. To use his own words, "The 
experiments were well made, but the results are 
negative ; " but he adds, '' I cannot accept them as 
conclusive." So the question remains to the present 
day ; and it is possible, as Faraday evidently believed, 
that the failure arose from the want of appliances 
sufficiently delicate to show the expected effects; 
although, if the opinion previously expressed in 
these lectures in regard to the nature of gravity be 
correct, it was the seeming analogy which was, at 
fault, as Faraday himself at times suspected. 

In his failures not less than in his successes, the 
example of Faraday may teach us most important 
lessons. A mind so subtile as his is apt to be capti- 
vated by fanciful resemblances; but he never fol- 
lowed vaguely the suggestions of analogy, inquiring 



GENERALIZATION. 269 

diligently at every step whither they were leading, 
and always submitting desire to the control of ex- 
perience. As thus curbed, analogy may be always 
safely followed; and as Bishop Butler so tersely 
wrote, *' Analogy is the very guide of life." She 
leads us when we are least aware of her guidance. 
She colors all our language. She determines half 
our thoughts. In submitting ourselves, as we must, 
to her control, let us consider well the situation ; and 
while we acknowledge our dependence, never part 
with our more precious birthright. Our guide is 
moulded of the same clay as ourselves; and there 
may be things in earth, as well as in heaven, not 
dreamt of in her philosophy. And, moreover, if 
harmony with nature be a test of reality, then har- 
mony with the spiritual life, then adaptation to the 
needs of the soul, is also a mark of certitude, an 
equally overpowering evidence of truth. 

Generalization in science is only a form of ana- 
logical reasoning. We are said to generalize when 
we ascribe to a class of objects qualities or relations 
which have been shown to be true of certain charac- 
teristic members of the class. Thus a certain num- 
ber of substances having a brilliant lustre, and to a 
greater or less degree ductile or malleable, and at 
the same time good conductors of heat and elec- 
tricity, which we class under the general name of 
metals, have been found after repeated trials to resist 
every attempt to decompose them, and are therefore 
regarded as elementary substances. Hence we con- 
clude that all metals are elementary substances ; and 
when a new one is discovered, as is not unfrequently 



270 GENERALIZATION. 



the case, we never think of attempting to analyze it, 
because experience with similar bodies assures us 
that all such attempts would be fruitless. 

Again, it has been shown by Davy, Wohler, and 
others, that alumina, magnesia, and several of the simi- 
lar earths are metallic oxides, and the metals of which 
they consist have been extracted and studied ; indeed 
aluminum and magnesium are now articles of com- 
merce and familiar to every one. Hence we con- 
clude that all amorphous powders resembling alumina 
and magnesia, and having like chemical properties 
are also metalliferous; so that when, within a few 
years, a large number of new earths were distinguished 
the chemist accepted them at once as metallic oxides, 
although in most cases the metal has not actually 
been isolated. 

Obviously, our assurance in all these cases rests on 
our confidence in the unity of nature's plan and 
method ; and the argument which convinces us dif- 
fers from the ordinary argument from analogy only 
in the extent of the ground covered. When Davy 
inferred from analogy that potash must contain a 
metal, and successfully followed out the suggestion, 
he reasoned from a comparatively superficial resem- 
blance between a few things to a deeper relationship. 
When we conclude that the new earths are metallic 
oxides, we reason from a wide knowledge of a class of 
bodies that a new substance, which has been shown to 
have the other qualities and relations of this class, 
also has an additional character, — though as yet un- 
observed, — which is common to all the other mem- 
bers therein grouped. The reasoning in the last case 



ALL KNOWLEDGE RELATIVE. 27 1 

is far more conclusive than in the first; but evidently 
it rests on the same assurance, the uniformity of nature. 
Prior to experiment Davy's inference was only proba- 
ble ; our conclusion is as certain as that the sun will 
rise to-morrow. In either case, however, the argu- 
ment is based on resemblances more or less remote, 
and the difference is one of degree and not of kind ; 
and so we may have every degree between the certi- 
tude of a far-reaching generalization and the mere 
suggestion of a feeble analogy. In science the merest 
hint may be of value ; for when in an investigation 
bewildered by complex conditions we are hesitating 
which way to turn, or what to try first, the faintest 
suggestion of analogy may decide us. On the other 
hand, in the relations of the spiritual life we must 
remember that even in our grandest generalizations 
we cannot escape from the material clogs of our mor- 
tal experience ; that all our knowledge is necessarily 
relative to our environment; and that though its 
material forms are doubtless symbols of higher reali- 
ties, yet these earth-born fancies can never be an 
exact picture of things spiritual, or a precise measure 
of things divine. 

Man lives in time, and he cannot release his 
thoughts from the fetters v/hich this condition im- 
poses. Continuous time and a corresponding con- 
tinuous change or growth are so inseparable from 
human experience that existence in time, with pro- 
gressive change, is the only mode of being of which 
the mind can form a concrete idea. We can reason 
and talk about a Being who is the same yesterday, 
to-day, and forever, and to whom a thousand years 



2/2 PRINCIPLE OF CONTINUITY. 

are as one day and one day as a thousand years, — 
we firmly believe in the reality of such a Being; but 
we cannot picture the existence to our minds, as the 
very imagery plainly shows. As we cannot escape 
from the limitations of matter, so we cannot escape 
from the limitations of time. As regards every event, 
the mind demands an antecedent and a consequent. 
The common axiom that ** every event must have a 
cause " is another phase of the necessity which the 
conditions of our environment impose on our being. 
The necessity is so interwoven in the complex web of 
material existence that we cannot dissociate it if we 
would. It is not a necessity of thought; for that 
Being who is from eternity to eternity the same had 
no antecedent and no cause. But it is a necessity of 
the imagination, and therefore a necessity of scientific 
knowledge. 

In science we call this lesson of experience " the 
principle of continuity," and it is a belief which 
exerts a profound influence on all our reasoning about 
material relations. It is this principle which alone 
gives strength to the doctrine of evolution ; but it is 
equally a controlling power in almost every depart- 
ment of scientific inquiry ; indeed it controls the 
very process of thought itself. 

Examples of continuity of action are all around us, 
and illustrations of the successful application of the 
principle in scientific reasoning might readily be 
cited. The science of geology is especially rich in 
examples of this class ; and our knowledge of the 
relative ages of strata, and of the succession of life on 
the earth, is in very large measure the result of tracing 



BREAKS OF CONTINUITY. 273 

out the evidences of continuous changes ; and in 
physics we often reason from what we can see to 
what we cannot see, through a chain of sequences 
which connects the parts of a continuous series, and 
thus exhibits relations which would be otherwise 
obscure. The same principle underlies all classifica- 
tion in natural history, and, as has been already 
said, is the warrant of the theory of evolution. 
Evolution is simply a wider growth, and is implied 
in the only conception of being of which the mind 
can frame a definite image. For our purpose, how- 
ever, it is not necessary to multiply illustrations ; and 
we turn next to some examples of the break of con- 
tinuity which have a much more important bearing 
on our subject ; for they indicate that beneath the 
obvious material relations there may be other influ- 
ences at work in determining the course of events. 

While we can usually safely follow the indications 
of continuity, yet, as in the case of analogy, we are 
frequently deceived, and even more frequently than 
in the application of the cognate principle ; and ex- 
amples of break of continuity present a striking feat- 
ure of nature which cannot be overlooked. Often 
the break is only apparent, resulting from the inabil- 
ity of our senses to follow changes succeeding each 
other with more than a certain limited rapidity. 
When a ball is fired from a rifled cannon it gains in 
the two hundredth part of a second its full and fearful 
velocity, and yet we know that while in the gun it 
passed through every stage of motion from indefinite 
slowness onwards. So also with molecular motions, 
which may last only some thousand milHonths of a 



274 CRYSTALLIZATION. 

second; between successive collisions all the phases 
of the recoil, the free path, and the rebound, must 
follow each other in due order. 

We do however find in nature phenomena which, 
after making every allowance for the imperfection of 
our senses, appear to be absolute breaks of continuity. 
One of the most striking of these is to be seen in 
the process of crystallization. I confess that I never 
witness the process without amazement. That out of a 
perfectly homogeneous and structureless liquid there 
should suddenly separate a perfect geometrical solid, 
with all its sparkling facets grouped with mathemati- 
cal exactness, is to me one of the greatest wonders in 
this world of beauty. The structure of a crystal is of 
course not so complex as that of a plant or an ani- 
mal; but then it has no gradual genesis; it has no 
antecedents ; it appears as a sudden break of con- 
tinuity ; its formation approaches as near to a sudden 
creation as anything we ever behold. This may seem 
to you inconsistent with what you have heard of the 
slow growth of crystals. But such statements apply 
only to the large, massive crystals, such as you may 
see in our museums, — some of which have doubtless 
been centuries in forming. I refer, on the contrary, 
to the sudden production of the minute crystals of 
which the larger crystals are gradually formed aggre- 
gates. These small crystals, when examined with a 
microscope, are seen to be as perfect as the larger 
specimens ; indeed, they are often far more per- 
fect; and they seem to drop out of the solution in- 
stantaneously, — the creation of each one, if I may 
dare to use the term, being in some cases attended 



DEFINITE PROPORTIONS. 2/5 

with a iiash of light as if to attest its mysterious 
origin. 

Another circumstance which sometimes attends on 
crystallization is even more indicative of a break of 
continuity than the facts I have mentioned. In the 
liquid menstruum, as it is called, the constituents of 
the future crystal are often mixed in variable propor- 
tions ; but the crystals which form unite these ingre- 
dients in absolutely definite proportions, conforming 
to the great law of combining proportions of chem- 
istry. This law in itself is probably the most general 
and striking break of continuity in nature. You may 
mix two substances, by solution or otherwise, in any 
proportions whatever, and there appears to be a per- 
fect interpenetration of the masses. Then when an 
electric spark, or some other cause, determines chem- 
ical union, these substances unite in certain constant, 
definite, and calculable, proportions, excluding the 
excess of one or the other ingredient; and this is 
what takes place in the example of crystallization 
just referred to. In order to reconcile this striking 
phenomenon with the principle of continuity, several 
chemists have endeavored to show that these definite 
proportions were merely a maximum effect of such 
restricted range that we failed to recognize the grada- 
tions ; and I have myself sought to test this sugges- 
tion by experimenting, — thinking that the range must 
be greater in proportion as the combining force was 
feebler, and that possibly in cases of weak chemical 
affinity it might be detected. But although at first I 
thought I discovered an indication of such an effect, 
my later experiments have proved that the propor- 



276 NATURAL AND SUPERNATURAL. 

tions are just as definite in weak compounds as in 
strong. I see therefore no escape from the conclu- 
sion that this apparent break of continuity is a real- 
ity; and should not such results teach us that the 
preconceptions of our experience are not infallible? 
Thus may even the study of science prepare us to 
recognize other possibilities of being than those of 
known material relations. 

That mode of being not directly cognizable by our 
senses we call the supernatural ; and we often reason 
as if it were something apart from and above nature. 
But is it not the more consistent theory that the su- 
pernatural and the natural are simply different phases 
of one system ; and that while with our bodily senses 
we apprehend only the material relations of this sys- 
tem, we can with our spiritual sympathies and aspira- 
tions reach out towards those higher associations 
for which this life is a preparation? Or may we not 
rather say that the supernatural embraces the natural, 
modifying in numberless ways the more obvious ma- 
terial relations, and thus constantly apprising us of' 
its omnipresence ; and do not such indications as we 
have been studying ever remind us that the material 
is not all of knowledge or all of life, and give us a 
confident expectation of more life and ampler knowl- 
edge behind the vail? 

When we fully comprehend that the fundamental 
conceptions comprised under the doctrine of con- 
tinuity are simply a product of experience, and 
dependent on material relations, we shall be able to 
think and reason more justly about spiritual relations 
in which the limitations of the material do not exist ; 



IDEA OF TIME. 277 



and although difficulties of conception may by no 
means be removed, yet a way is opened by which 
the seeming contradictions of theological doctrines 
with our experience may possibly be reconciled. 

As has already been intimated, we have no expe- 
rience, and therefore no actual knowledge, of any 
state of existence, except of that in which continuous 
change and growth constitute the invariable order 
of being. Our idea of time is simply a conception 
based on the succession of events. The fundamental 
conception of duration arises unquestionably from 
the succession of thoughts in our own minds. It is 
thus that we reach an idea of short duration, as of 
the swing of a pendulum; and it is only of such 
durations that we can be said to have any direct 
consciousness. Longer durations are to us simply 
the multiples of siich short intervals as we can di- 
rectly perceive and appreciate ; or else have known 
relations to the periods of events which we assume 
as the standards of measure. The day is the period 
of the rotation of the earth on its axis ; the hour is 
one twenty-fourth part of a day, the minute the one 
sixtieth part of an hour ; the second the one sixtieth 
part of a minute, and at any given place is the dura- 
tion of the swing of a pendulum (about one meter 
long), whose exact length is easily adjusted. It is 
only this smallest unit of which we can be said to 
have any direct perception. Our knowledge of much 
larger periods, however exact, is purely formal. 
When a boy learns that a year is the period of the 
revolution of the earth around the sun, the most he 
gains is the idea that this, to him already familiar 



278 TRUE MEASURE OF LIFE. 

period in human relations, during which the succes- 
sion of seasons is completed, is the duration of a 
continually recurring astronomical event. Nor does 
his knowledge become any more real when he is 
further informed that the year comprehends three 
hundred and sixty-five days, five hours, forty-eight 
minutes, forty-seven and seven tenths seconds. But 
he can be thus impressed with the fact that the 
durations of the events by which time is measured 
bear a constant relation to each other, and hence, be 
led to the conclusion that the quantity measured is 
a real attribute of material relations, and hence, also 
of material life. 

A very few considerations, however, will show that 
time is solely an attribute of material relations, and 
no adequate measure, even of that phase of our 
spiritual life which terminates with the death of the 
mortal body. Conventionally, we measure man's life 
in years ; but who does not recognize that Raphael, 
dying at thirty-seven, or Pascal, dying at thirty-nine, 
lived not only a richer, but a really longer life than 
most of the Methuselahs and Nestors of history. He 
lives longest who is able most fully — 

" To crowd the narrow span of life, 
With wise designs and glorious deeds." 

Life should be measured not by years, but by 
thoughts, events, and deeds. The succession of 
thoughts in the mind is a far more accurate measure 
of conscious duration than the beats of a pendulum ; 
although as compared with the standard of time, the 
flow of thoughts is so variable, not only in the minds 



RAPIDITY OF THOUGHT. 279 

of different men, but also in our own minds under 
varying conditions. After some critical experience, 
how often do we say that we have lived longer during 
the past day or week than during months or years 
before ; and these words are no mere figure of speech, 
but on the contrary express an important truth. 

During our mortal lives, the rapidity of thought is 
limited by our physical organization; but we can 
easily conceive that it might be indefinitely in- 
creased ; and such conceptions appear in part to be 
reahzed both in the phenomena of dreams, and in 
the experience of drowning men ; who, when subse- 
quently resuscitated, often have said that, during the 
brief interval before they became unconscious, the 
whole course of their lives flashed through the mind. 

Could we increase the rapidity of thought, we 
should increase the conscious duration of life during 
a given time ; and it is a perfectly rational concep- 
tion, that with a finer organization the life of a cen- 
tury might be crowded into a day. Obviously, we 
can apply magnifying power to time as we can to 
extension. As under our microscopes, an area 
barely perceptible to the eye becomes spread out 
into a broad plane, teeming, it may be, with life, so 
we can conceive that a duration barely perceptible to 
our senses may be to a more dehcate organism a 
period of vast activities. 

" Alike in God's all-seeing eye. 
The infant's day, the patriarch's age." 

Magnify, now, duration indefinitely, not by extend- 
ing time, but by crowding activities into the present, 
19 



280 LIMITATIONS OF TIME AND SPACE. 

and you annihilate time, — or rather, you eliminate 
the element of time from the spiritual life ; and such 
considerations will lead the mind to recognize the 
truth that eternity consists not in limitless time, 
which would be unendurable, not in passionless con- 
templation, which would be weariness, but in the 
removal of the Hmitations of time from our mental 
activities. Time, like space, is an attribute of material 
relations; and although in this Hfe even our mental 
processes are controlled by the limitations which 
these relations impose, and although the imagination 
can form no distinct image of a state of being freed 
from the limitations of time and space, yet we are 
able by such considerations as we have here imper- 
fectly presented so far to dissociate in our thoughts 
these conditions from our spiritual life as to recog- 
nize the aptness of the imagery by which such a 
state is prefigured in the Scriptures, and also to ad- 
mit the possibility of spiritual relations which to our 
material vision seem to be contradictory. We can- 
not be said to have actual knowledge of any state of 
being unconditioned by time and space; but the 
circumstance that we are able to recognize some of 
the attributes of such a state is in itself weighty 
evidence of its reality. 

To a being freed from the limitations of time there 
are no beginnings and no ends ; or rather, those tran- 
sitions which to us appear as the beginnings or the 
ends of events, are simply phases of the ever present 
and the ever actual. God's prescience is not fore- 
knowledge, but actual knowledge. He seeth the end 
from the beginning, because both are ever present; 



FREE WILL. 28 1 



and His knowledge is not inconsistent with man's 
free will, because that will is limited in its exercise 
by the very conditions of time and space which the 
Creator has imposed on the material universe. 

In all material relations man's free will is a definite 
factor, as much so as any other form of energy ; and 
the final attitude of man's mind towards his Maker is 
equally within his own power of determination ; but 
here man's prerogative stops. Man as a living creat- 
ure has a subordinate power in the material creation. 
Man as a living soul may regulate the attitude of his 
mind to other living souls ; but however completely 
he may control actions, he cannot force the wills even 
of those nearest and dearest to himself. In a word, 
his will has control only over material relations and 
over himself; and to one who does not wait on re- 
sults, but who sees at once every stage of our material 
processes and of our mental conflicts, the foreknowl- 
edge of events may be perfectly consistent with the 
freedom of His subordinate actors in the drama of 
human life. The architect, who in his imagination 
sees his building completed in all its details, may be 
said to have a foreknowledge which is compatible 
with a large degree of freedom among the workmen 
in their respective spheres ; and although this illus- 
tration fails in essential details, it may serve to pre- 
figure that fuller prescience when the limitations which 
here exist are removed. 

Such illustrations do not of course remove the diffi- 
culty we have in conceiving of a being freed from the 
limitations of time ; and, by dwelling on the thought 
that it is impossible that we should be free if God 



282 UNREALIZED INFERENCES. 

foresees all our actions, we can easily make the in- 
compatibility appear as marked as ever. All that we 
can hope is to recognize the possibility of conditions 
which may make such relations intelligible, without 
expecting to comprehend them. Free will is a fact 
of consciousness, and such considerations as we have 
advanced make God's foreknowledge a clear inference 
of our intelligence from facts of consciousness ; and 
here as elsewhere we must be content to accept our 
limitations, and wait for the clearer day when we shall 
know even as we are known. 

It is not solely in spiritual relations that our reason 
leads us to inferences which lie beyond the powers of 
conception. This is equally the case in the higher 
forms of mathematics, where, as we have before said, 
we often deal with relations, like the higher dimen- 
sions of multiple algebra, of which it is impossi- 
ble for the mind to form any distinct idea ; and no 
mathematician questions that these relations are re- 
alities, yet he can only describe them by inadequate 
and figurative language which deals with types and 
symbols. 

This power of the human mind of reaching out in 
various directions beyond its own experience, to rela- 
tions of which it can form no concrete and material 
images, is to my own mind one of the strongest evi- 
dences of the reality of a higher life in which these 
dim visions shall be realized. 

We do not, however, care to deal with theological 
subtleties ; but the overlooking of the distinction be- 
tween the material and the immaterial, which we have 
attempted to emphasize, has led to a fallacy in much 



MISTAKEN PRECONCEPTION. 283 

of the reasoning about the genesis of nature which it 
is important to expose. 

We can form no clear conception of any act except 
as taking place at a given time. The battle of Water- 
loo was fought June 18, 1 81 5. America was discov- 
ered on the 1 2th of October, 1492. Julius Cassar 
was assassinated in the ides of March, 44 B. c. The 
battle of Marathon was fought September 28 or 29 
(according to somewhat uncertain computations), 
490 B. c. ; and the popular belief is that the world 
was created at an equally definite date in the remote 
past, which could be stated in equally precise chro- 
nology if we only had the knowledge. At the basis 
of this belief is a tacit assumption that all intelligence, 
the Creator as well as the creature, must act under 
the limitations of time. " God spake and it was 
done ; " and we assume that the word of the Creator, 
like the word of man, was spoken at a definite mo- 
ment in the succession of events which measure 
time. But science shows that the genesis of the 
world was a process of gradual growth ; and the in- 
consistency of this conclusion in a great variety of 
phases with man's preconception of the mode of 
creation, has always been a hindrance to faith. 

It is by no means perfectly clear how such a gen- 
eral preconception arose. It certainly did not come 
from the study of nature ; for, as has been said, the 
whole scheme of nature, so far as we understand it, 
is wholly at variance with such an idea. Growth is 
the order of nature ; and although as yet no man has 
been able to discover any distinct and unquestionable 
traces of the first introduction of a new species into 



284 ORIGIN OF THE PRECONCEPTION. 

the world, yet it cannot be seriously questioned that 
the theory of the gradual development of organic 
types is in harmony with all that we know of 
biology. 

Nor does it appear probable that the preconception 
came from the Hebrew Scriptures ; for although in 
Genesis it is distinctly declared that all things were 
created by Jehovah, the great " I Am," the mode of 
creation is described in such obviously figurative lan- 
guage that no difficulty has been found in reconciling 
it with any result of science when once clearly estab- 
lished. Nevertheless, it is very generally assumed 
that a creation " ex nihilo " at a definite moment of 
time is expressly declared in the Bible, and on this 
basis it is constantly urged, in answer to the appar- 
ently irreconcilable evidence of science, that the 
Almighty could instantly call a universe into being 
out of nothing if He chose. Granting a clear revela- 
tion, such a plea might be relevant. But there is no 
such clear revelation ; for admitting whatever author- 
ity the most extreme literalist may claim for the 
Pentateuch, it must be conceded that the language 
of these early books admits of the most diverse inter- 
pretations ; and the mode of creation still remains an 
open question for scientific investigation. The ques- 
tion is not how to reconcile observation and revela- 
tion, but to find out as far as possible what the facts 
really were. 

If, then, the preconception cannot be traced either 
to a distinct revelation, or to the observation of na- 
ture, must it not result from the normal action of the 
human mind under its limitations? In all human 



god's creation not as man's creation. 285 

relations creation, whether in art, in literature, or in 
science, implies effort, often long-continued effort, 
which taxes all the strength and all the perseverance 
that the most gifted men can command. There are 
obstacles to be overcome, and there is a conscious- 
ness of weakness and inefficiency, which ever reminds 
us of our limited powers. Moreover, at most our 
creation consists in transforming old materials into 
new shapes. The potter moulds the clay ; the sculp- 
tor chisels the marble, and both clothe with beauty 
the rude materials on which they work ; but all the 
while they are painfully conscious of the limitations 
which the material imposes on their art. It is nat- 
ural, therefore, to think of the Almighty as a power 
before which all obstacles yield without effort, and 
which can call order and beauty not only out of chaos 
but out of nothing. There is, however, an illusion 
which vitiates this inference; and the old apho- 
rism " Ex nihilo nihil fit " is much nearer the truth. 
The error consists in overlooking the limitations of 
time by which we are circumscribed, but which can- 
not bound the Creator. Our times are in His hands ; 
but God himself does not work in time. " God work- 
eth hitherto and I work," said the Saviour; but He 
worketh not as man worketh. "He seeth the end 
from the beginning, and looketh under the whole 
heavens ; " and what to us appear as consecutive and 
consequent are to Him parts of a plan whose pur- 
poses will be fully revealed only when time shall be 
no more. 

The view, therefore, that a theory of creation by 
slow development derogates from the attributes of 



286 "ETERNAL GENERATION." 

the Almighty is a pure illusion resulting from our 
limitations. To Him who inhabiteth eternity pur- 
poses are valued, not as they seem to ripen fast or 
slowly to us, but according to their beneficent de- 
sign. God, who is ever present throughout all time 
both to will and to do of His good pleasure, compre- 
hends our temporal relations in His all-embracing 
Providence, and adopts methods in view of the uni- 
versal, and not solely of a temporal good. 

In all material relations we have every reason to 
believe that the knowledge we have acquired is accu- 
rate and trustworthy ; but in speculating about spirit- 
ual relations, we must always remember that we are 
liable to be deceived by the aberrations of our mate- 
rial vision; and we cannot safely build a theory of 
the universe on such treacherous foundations as our 
preconceptions of the methods of the Divine govern- 
ment can alone furnish. 

The conception of the creative power as acting 
through an indefinite time, or rather as independent 
of time, was familiar to Origen and the other Nicene 
fathers, and was embodied by them in the famous 
doctrine of the " Eternal Generation," which, although 
usually limited to the second person of the Trinity, 
was by Origen, at least, extended to the material 
creation. 

The recognition of this doctrine as applicable in 
some limited measure to the genesis of nature would 
tend very greatly to reconcile the systems of theology 
with the systems of science. For if the theologian 
accepts the eternal generation of the Son as one of 
the most fundamental of his tenets, how can he con- 



ALL KNOWLEDGE IN HARMONY. 2Sy 

sistently find fault with the analogous doctrine of 
science which involves a similar idea? 

We do not advance the doctrine of the eternal gen- 
eration of matter as positive knowledge, or even as 
a legitimate inference of science ; but we do claim 
that it is a possible inference from the observed facts 
of nature, and that it is in entire harmony with the 
most profound dogmas of theology. 

Such speculations may have little value towards 
establishing truth ; but they at least show how foolish 
it is to set theological dogmas in opposition to sys- 
tems of science. All real knowledge must eventually 
be found to be in harmony, and the only way to find 
truth is to seek it with untiring effort, and to keep 
the mind unbiassed by any theories during the search. 
The path is difficult, the labor exhausting, and with- 
out faith in eternal verities the investigator will soon 
lose heart, and abandon the search. If, however, 
with singleness of purpose the student keeps the one 
great aim in view, and not only has faith in truth 
but the courage to face it in whatsoever guise it 
may appear, he will gather strength as he pro- 
ceeds; and, although his vision in this life may be 
restricted, and he may not rid himself of earthly 
clogs, yet in the end he will at least be satisfied 
that throughout the universe of being One Mind 
ruleth over all. 

Moreover, such speculations may have this positive 
result in so far as they show that time is not the 
measure of spiritual being. There are often periods 
in Hfe when crowding opportunities demand more 
time than we have to give. But taking life as a whole 



288 MORE LIFE. 



there is time enough for all we are able to accomplish, 
and it is more energy, and not more time, that we 
really need : — 

" 'T is life of which our nerves are scant ; 

More life and fuller, that I want." 



THE TWO SYSTEMS. 28g 



LECTURE X. 

THE SYSTEMS COMPARED, — RELIGION AND 
SCIENCE. 

TN the necessarily imperfect sketch of scientific 
-*- methods which has been given in the previous 
lectures, my main purpose has doubtless been obvi- 
ous from the first; and I think it must have clearly 
appeared that the speculative objections to Christian 
belief which are so confidently set forth are no 
greater than must be encountered in every depart- 
ment of abstract thought, and are inseparable from 
our material relations. The close resemblance in this 
particular between the systems of science and the 
systems of religion presents, as it seems to me, by 
far the most cogent of the evidences of natural the- 
ology ; and after examining the features of the scien- 
tific systems it remains to bring together the separate 
threads of the discussion and present the opposite 
side of this very striking analogy. 

I enter, however, on this part of the task I have 
undertaken with great diffidence. Thus far I have 
been, for the most part, on my own ground ; now I 
pass over on to yours. And at the same time I feel I 
ought to change positions, and in this distinguished 
school of theological learning to seek instruction, and 
not attempt to teach. I feel, moreover, that my 



290 POSITION TAKEN. 



education in great measure unfits me for the office 
which I temporarily fill; and as it is impossible that 
I should see the subject from your point of view, I 
fear that I may weaken the force of my argument 
by overlooking features which you deem important; 
or even involuntarily offend by ignoring doctrines 
which you deem essential. While I feel the firmest 
assurance of the underlying truths of Christianity, and 
the deepest respect for every honest conviction, still 
I must confess that my whole education has made it 
impossible for me to attach the same importance to 
details of doctrine, or forms of ceremonial, as do 
those who have been trained in a different school, 
though I would not by any hint of mine wound the 
sensitive realist, or the conscientious ceremonialist. 
I say this without the least assumption of greater 
freedom, or suspicion of complacency, — freely ac- 
knowledging that the judgment of those who minister 
to spiritual needs is much better established, and not 
questioning that their spiritual insight is far deeper 
than mine. 

In my own province of thought I know so well 
how an exact knowledge of relations will often set 
aside judgments which a superficial knowledge might 
seem to justify, that I am fully sensible that the same 
principle must hold in other departments of learning 
equally ; and I therefore offer the argument I have to 
make simply as a suggestion, — feeling sure that it 
will receive your thoughtful consideration, and be 
accepted for all it is worth. Nevertheless, I have 
thought — otherwise I should not be here — that 
a certain advantage might arise in presenting the 



THE ARGUMENT STATED. 29 1 

subject -from a point of view different from that in 
which a theological student is accustomed to regard 
it; and that the opinions of a student of science, who 
had given much thought to such questions, however 
crude his theology, might help you to meet similar 
questions which sooner or later in your ministry will 
be forced by thoughtful men on your attention. I 
may overestimate the strength of my argument, — for 
the force of an analogical argument depends very 
greatly on the previous experience of those to whom 
it appeals, — but it has come home with overpower- 
ing force to my own mind; and I find it difficult to 
conceive how any one who has felt the bewilderment 
of scientific uncertainty, as well as of religious doubt, 
can resist its cogency. Take out the elements of 
feeling, affection, and faith, and the last is to me no 
more oppressive than the first. 

The argument itself may be stated in a few words. 
As there are systems of science, so there are systems 
of religion ; and among these, one both intellectually 
and morally so far in advance of the others that 
it alone claims the consideration of educated men. 
Regard now the Christian religion simply as an 
external fact, as an existing spiritual, moral, or in- 
tellectual force, independently of all supernatural 
sanctions, or superhuman obligations, and all must 
admit that it is the greatest power in the world. 
However originating, or however appointed, there is 
no power over men's minds and hearts which can 
for one moment be compared with it. Throughout 
Christian lands this power is everywhere pervasive, 
and even in lands not recognized as Christian its 



292 THE ARGUMENT STATED. 

indirect influence has softened the asperities of bar- 
barism, and mitigated the cruelties of savage Hfe. 

Compare, in its mere external or intellectual as- 
pects, Christianity as a system with gravitation. 

As the way was prepared for Newton, so was the way 
prepared, and in a most remarkable manner, for the 
Founder of Christianity. For centuries before His 
coming all that was purest and noblest in the world's 
thought was leading up to the expected Messiah. 
Then as the greatest advance ever made in the 
knowledge of material things came by one man, 
who greatly raised the level of scientific thought, so 
Christianity came like a great induction of spiritual 
truth, which so greatly raised the level of spiritual 
thought that after nearly two thousand years the 
Christian world does not yet appreciate the elevation 
that was reached. 

As modern science dates from Newton, so all that 
is noblest and best in man, all that is pure and lovely 
in life, all unselfish morality, all heroic chivalry, all 
holy charity, is dated Anno Domini. 

The Founder of Christianity was no mythological 
hero ; but, whatever views we may entertain of his 
nature, he was in form and likeness a man, living at 
one of the best known epochs of the world's history ; 
and every account of his character is in perfect har- 
mony with his elevated doctrines and momentous 
declarations. 

That doctrine and those declarations present diffi- 
culties of conception. We cannot reconcile them 
with our experience of natural relations ; and in the 
same way we cannot reconcile the system of gravi- 



THE ARGUMENT STATED. 293 

tation wjth our knowledge of the mode of action of 
the other forces of nature. 

While, however, there are these difficulties of con- 
ception, the practical application of Christian doc- 
trine as a rule of life, like the use of the principle of 
universal gravitation in astronomical computations, is 
perfectly simple and definite. Indeed, Christianity 
was revealed as a life, and has been handed down to 
us pure and undefiled in the lives of its disciples. 

Like systems of science, Christianity deals with 
symbols, which are obviously the signs of realities 
in their essence incomprehensible by man ; and even 
if — as does at times happen in both cases — the sign 
is mistaken for the substance, still such symbols are 
of the very greatest value in aiding the imagination 
and guiding the thought. • 

Newton so greatly raised the level of astronomical 
conceptions that since his time astronomers have 
been fully occupied in deducing the consequences of 
his great induction; and so, since the Christian ages 
began, apostles, saints, and fathers, with lowly and 
learned men of every name and calling, have been 
diligently unfolding the beauties, the marvels, and 
the glories of the truth that was then revealed. No 
wonder that the interpretations did not always agree, 
that bitter controversies arose, and that men profess- 
ing the faith used power and influence as instruments 
of oppression and persecution ; for the same sad feat- 
ures have disgraced the history of science, without 
the excuse of intense feeling to inflame passion or of 
blind fanaticism to obscure reason. But as in spite 
of follies and quarrels astronomy has grown to be a 



294 THE ARGUMENT STATED. 

noble science, worthy of the most gifted human in- 
telligence, so in an immeasurably greater degree the 
Christian Church through weakness has been made 
strong, and has become a holy temple in which the 
loftiest aspiration finds satisfaction, the purest affec- 
tion repose, and unsullied charity its full reward. 

Lastly, as the system of gravitation has been tested 
and ratified by the complete accordance of natural 
phenomena with the deductions that it involved, so 
has a most commanding seal been set on Christianity 
by the entire harmony of the system with the spir- 
itual needs of man. It is in that harmony that all 
its strength lies. It has been tested by the most 
varied experience. The blood of the martyrs has 
been the seed of the Church ; and the attestation of 
the great army of its confessors rolls down the Chris- 
tian centuries with ever louder shouts of rejoicing 
and songs of thanksgiving and praise.^ 

While thus wonderfully adapted to man's spiritual 
needs, so just in proportion as our knowledge be- 
comes enlarged, and our insight deepened, is Chris- 
tianity found to be in harmony with all truth. The 
most gifted minds and profoundest scholars the world 
has known have not only confessed Christ before 
men, and acknowledged Him to be the Lord, but have 
also testified that increasing acquirements and widen- 

^ This test of experience, so clearly recognized in science, is 
also accepted in theology ; and even Roman Catholic doctors 
admit that the decrees of Councils must be accepted by the pub- 
lic mind of the Church before they can be declared the voice of 
God. As early as the fifth century Vincentius Lirinensis laid 
down as the test of authority: *'Quod semper, quod ubique, 
quod ab omnibus creditum est." 



CHRISTIANITY A FACT OF NATURE. 295 

ing vision brought an ever deeper conviction of His 
truth. 

If, then, man can in any case rely on his experi- 
ence as a test of truth; if harmony with nature is 
any evidence of participation in the scheme of na- 
ture ; if this world is not wholly a phantom and a 
deceit; if all knowledge is not equally delusive, — then 
the essentials of Christianity must be true. Such is 
the argument. You must have anticipated it as I 
traced out the features of scientific systems ; and I 
have only to add, before concluding this course of 
lectures, some connected thoughts which may serve 
to enforce or illustrate special points of this strik- 
ingly close analogy. 

Remember, in the first place, that we are here 
treating Christianity as a fact of nature, as an exist- 
ing system of religious truth, on the same plane as 
any other system of knowledge ; and from this point 
of view only do we compare it with systems of sci- 
ence, like the system of gravitation. We all believe 
that Christianity has other sanctions and attestations ; 
but in a question of Natural Theology we leave ail 
this evidence on one side, and deal with Christianity 
only as an external fact of nature, as an historical 
phase in the development of humanity, as a system 
of morals, as a system of philosophy, or as a guiding 
and directing motive which controls large masses of 
mankind. I trust that I am not misunderstood; 
although there is an obvious rhetorical difficulty in 
dealing with the subject in this way. My language 
might very easily be misconstrued, although I have 
earnestly endeavored to avoid the occasion. No one 



296 CHRISTIANITY A FACT OF NATURE. 

who has deep religious feeling can associate even in 
the most indirect way Christianity with a system of 
science; or the Founder of Christianity with the 
originator of such a system, however great and 
worthy, without feeling the incongruity which the 
comparison involves; and it is difficult to find lan- 
guage which shall convey my meaning without a 
suggestion of irreverence. You will, I am sure, ap- 
preciate the difficulty and pardon any infelicity. 

We are dealing solely with the evidence of nature, 
and we must treat Christianity as a part of nature, 
just as gravitation is a part of nature, if we would 
estimate the value of the evidence which nature alone 
can give apart from all other sanctions. Of course 
other evidences have their due place, and to most 
minds have such a paramount authority as to wholly 
hush the feeble voice of nature. But I am here to 
show you, as far as I am able, how forcible the tes- 
timony of nature is by itself, apart from any super- 
natural credentials ; and I affirm that Christianity as 
an external fact is a part of this evidence. Chris- 
tianity is a definite force in the world, and is as 
essential a factor in the development of humanity, 
as steam-power, electricity, or natural selection. 
The supernatural evidence of Christianity is wholly 
additional to the sanctions we urge ; and the former 
is rendered vastly more credible and persuasive by 
the evidence of nature. If you can remove the ante- 
cedent presumption against the miraculous, you 
place at once the overwhelming historical evidences 
of Christianity on the same basis as all other his- 
torical testimony ; and how can you accomplish this 



THE ULTIMATE TEST OF TRUTH. 297 

SO effectually as by showing that the resulting system 
is in entire harmony with what are always regarded 
as earth-born systems? 

I must, however, myself protest against the last 
term, while using it to point a distinction. I believe 
most firmly that all truth is one and inseparable, 
and that there is no real distinction between heaven- 
born truth and earth-born truth. I believe that in 
the strict sense of the term, gravitation was as much 
a revelation to man as Christianity. I cannot, there- 
fore, call one human and the other divine. Grant 
the widest difference between the modes by which 
the revelations were communicated. Grant that the 
very diverse nature of the revelations required this 
difference; yet in either, case the truth is God's 
truth ; and in the last analysis, the ultimate test of 
all truth must be its universal and perfect harmony. 
To me the most weighty evidence of Christianity is 
its supreme naturalness ; that intensely human life in 
the past, that Holy Church ever since, in perfect 
harmony with all my purest affections and loftiest 
aspirations, is the strongest assurance of truth, — and 
truth is always and every\vhere divine. 

Again, Christianity as a fact of nature involves all 
prior questions as to the personality of the Godhead, 
or the attributes of Deity. We have no occasion to 
go back to questions of design, or plan in nature. 
We deal with the most conspicuous design, the most 
wonderful plan; and if these are shown to be of a 
piece with the rest of nature, why need we further 
testimony? In the first lecture of this course, we 
endeavored to show that all arguments from adapta- 



298 ADAPTATION TO MAN'S WANTS. 

tion or from general plan were inductions based on 
analogy; and that like other inductions their force 
depended on the fulness with which they harmonized 
the facts of nature. We claim for our present argu- 
ment the same validity; and if the claim is allowed, 
the argument has a far greater range than any pre- 
vious argument of natural theology; for it secures 
all that Christianity, as an external fact of nature, 
can be justly claimed to include. And looking at 
the question in its simplest aspect, why is not the 
adaptation of Christianity to man's spiritual wants as 
direct an evidence of design as the adaptation of 
the eye to seeing, or the lungs to breathing? — and 
regarding the plan of redemption simply as it was 
first exhibited by the life and death of Christ, and as 
it has been exemplified in the lives and deaths of 
saints and martyrs ever since, as conclusive an evi- 
dence of intelligence as the plan of the vertebrate 
skeleton, or the spiral distribution of leaves on the 
stems of plants? 

We have in the most positive manner afifirmed 
that inductions based on analogy or otherwise are 
not, and from the nature of the case cannot be, dem- 
onstrations; and have shown that they may offer 
every degree of conclusiveness depending on their 
agreement with the phenomena of nature. We could 
have no more perfect accordance than Christianity 
offers. But however conclusive such evidence, there 
is always room for speculative doubt ; and we freely 
admit that our argument is not a proof, but it affords 
all the certainty we can have in natural theology. 

As I have before said, it is a striking fact in regard 



THE WAY WAS PREPARED. 299 

to all scientific inductions that they never come to 
fruition until the time is ripe. If premature, they 
fall on barren soil, and the numberless anticipations 
of genius are well-known illustrations of this truth. 
And when we consider the obvious law of progres- 
sion which the development of knowledge obeys, we 
are forced to recognize that individual men, however 
great their genius, are not essential to the result. 
Like the prophets of old, they are interpreters of a 
preordained purpose. No one can question that the 
law of gravitation would have been discovered within 
half a century, if Newton had not lived ; and, great as 
his influence has been, and greatly as he hastened 
the progress at the time, astronomy would certainly 
have been as far advanced to-day if the work had 
been left for other hands. Since the time of Hippar- 
chus the way had been preparing for the great in- 
duction; and Isaac Newton was the name given to 
the faithful and gifted servant who was born into 
the world when the time was ripe. 

Again, how striking the analogy with the coming of 
Christianity ! Here also the way was prepared. " But 
when the fulness of the time was come God sent forth 
his Son, made of a woman, made under the law;" 
and although the messenger was the Divine Son, and 
the message was the redemption of man, yet the gos- 
pel came in the same simple naturalness with which 
every great truth has come to the world. Before 
John came crying in the wilderness, how long, how 
tedious, and how devious, had been the way, how 
halting the progress ; yet from time to time seer and 
prophet had caught glimpses of the coming truth as 



300 THE COMING. 



they diligently toiled in the vineyard, and sought to 
make ready for the vintage of the Lord. 

As I ponder this sublime history I cannot resist 
the impression that this conformity to natural methods 
is an irresistible evidence of genuineness which we 
cannot afford to overlook. God introduced Chris- 
tianity into the world by the same methods by which 
He has opened to us all knowledge, — in order that 
He should not confuse the understanding, or confound 
the intelligence, of His creatures ; and thus it is that 
our expanding science becomes to us on a lower 
scale a type and similitude of the methods of Divine 
revelation; and the certitude of the one gives us a 
confident assurance of the certitude of the other. 

It was because I wished to set forth this analogy 
in a strong light that I dwelt at some length on the 
prelude to the discoveries of Newton, — in order that 
you might see that his way was prepared by methods 
not always direct, and by servants not always worthy, 
and yet that all conspired to ensure the final result ; 
and that thus you yourselves might draw out the anal- 
ogy with a power which I am unable to command. 

In entire harmony with the perfect naturalness of 
the whole dispensation was the coming itself. It was 
not in an obscure period of human history, or in a 
remote corner of the earth ; but in the midst of the 
Roman Empire, and during the Augustan age of the 
ancient civilization. The coming was not heralded 
by signs and portents which inspired awe and com- 
manded attention ; but in all the simplicity of child- 
hood, and in all the naturalness of growth. What a 
lesson is there in the simple statement that " the 



GRADUAL UNFOLDING. 30I 

child grew, and waxed strong in spirit." And so un- 
obtrusive and unobserved was this growth, except 
by a few humble peasants, that when the glory of His 
mature powers broke upon the Jewish world it ex- 
cited the wondering remark, " Whence hath this man 
letters, having never learned?" 

In respect only to this natural growth, but as a 
further incidental illustration of the fact that the most 
glorious of all advents came to the world with entire 
conformity to natural methods, allow me in all rever- 
ence again to call your attention to the striking cir- 
cumstance in the life of Newton, upon which I have 
before dwelt, — that we find him, while still a college- 
student, in possession of mathematical power, and of 
a new calculus, not only far in advance of his teachers 
but also of his age. The advent of new truth has 
always been by the same gradual unfolding ; and is 
there not the strongest antecedent presumption that 
He of whose fulness we all partake should in His 
mediatorial office conform to the same methods He 
had Himself ordained? And is not the harmony of 
the result with this antecedent presumption the 
strongest possible evidence of genuineness? Would 
man's invention in a pre-Christian age ever have 
conceived of such a method or pictured such a 
likeness ? 

The feature which above all things else is most 
striking in a great induction is that such an advent 
raises the level of human thought. Therefore such 
inductions mark epochs in science. Astronomy 
points back to Newton; and no one can question 
that for years to come natural history will point back 



302 ANCIENT AND MODERN CIVILIZATION. 

to Darwin. How is it with religious thought? The 
comparison may seem almost irreverent ; and yet it is 
highly instructive. Looking at Christian institutions 
simply as outward facts, without regard to sanctions, 
dogmas, doctrine, or creeds of any kind, what do we 
see? No less than this : that everything in the world 
which is loftiest and profoundest in thought, which 
is most ennobling and heroic in character, which is 
bravest and most unselfish in action, which is purest 
and loveliest in art, which is most consoling or hope- 
ful in philosophy, and above all this, every form of 
beneficent charity, every movement for the amelior- 
ation of mankind, every influence which sanctifies 
family ties, dates from one conspicuous and definite 
epoch of the world's history from which civilized 
men began to count anew the revolving years. 

I certainly need not in this place attempt to draw 
a parallel between the ancient and the modern civili- 
zation, to show how great a change was wrought, and 
how great an elevation was reached in one short life. 
But if in the interest of natural theology I can induce 
you to look at the subject from my point of view, 
and for the sake of argument to consider the claims 
of Christianity as simply an external feature in human 
society, I hope I may render a real service by giving 
you the command of a very powerful argument which 
can be pressed, not only without compromising or 
invalidating any supernatural evidences, but on the 
contrary, which will furnish a secure basis on which 
such claims can be established. It must be that a 
system which is so obviously a part of nature has the 
same authenticity as the rest of nature; and then 



NATURE AND THE SUPERNATURAL. 303 

comes- home with redoubled force the old argument 
that men unaided could not have raised themselves 
by one leap to such an elevation. 

Even in regard to scientific discoveries it inspires 
confidence to know that the investigator was in full 
relations with his subject, and in all respects equal to 
his work; and we have shown how conspicuously 
this was true in the case of Newton. But who can 
*• speak the matchless worth " of the Founder of 
Christianity? Certainly not a layman in this place. 
It is to be your great privilege to rehearse this story ; 
and, as told by your lips, in simplicity and power, 
may it bring consolation, comfort, and conviction to 
many a weary and troubled soul. In seeking to 
make evident that " Nature and the Supernatural," 
are "The one System of God," a most gifted and 
spiritually minded American clergyman, the late 
Horace Bushnell, has sounded forth the glories of 
that wondrous tale " in notes almost divine ; " and in 
following his chaste, beautiful, and effective presen- 
tation of the character of Christ, the one feature that 
most impresses the reader is its supreme naturalness. 
The consciousness of power is all there ; the mystery 
of personality is all there ; the terror of justice is all 
there ; the awfulness of sacrifice is all there. But it 
is the sweetness of affection, the tenderness of com- 
passion, the earnestness of pity, the fervor of charity, 
the ardor of zeal, the devotion to duty, the submission 
to authority, the perfection of manhood, which rivets 
our attention, which engages our sympathies, which 
commands our reason. 

All systems of science, as we have seen, present 



304 DIFFICULTIES OF CONCEPTION. 

insuperable difficulties of conception, because mate- 
rial relations are the measure of our experience and 
therefore the measure of our positive knowledge. 
Can we expect that the philosophy of religion will 
be more intelligible? And the more we study, the 
more plainly it will appear that in this respect also 
the two orders of truth present a most striking anal- 
ogy ; and that in either case the difficulties arise from 
the impossibility on our part of picturing to the mind 
any relations not realized in our own experience or 
in that of our fellow-men. Even in regard to material 
relations there is a great difference among educated 
men in the power of realizing unseen conditions ; and 
to rude, unimaginative folk nothing exists beyond the 
range of their immediate perceptions. With those 
whose imaginative faculties have been most cultivated, 
the limit of power is soon reached ; and however 
much the philosopher may speculate about trans- 
mundane realities, and however firmly he may believe 
in them, he can form no mental images of such beings 
that are not painted in colors of clay. Hence it is 
that I have dwelt so fully on the difficulties of con- 
ception which the fundamental concepts of physical 
science present, — in order that you might appreciate 
how very close is the analogy which I am endeavoring 
to enforce. 

The incongruities and apparent inconsistencies 
which the systems of science involve do not invali- 
date their essential truth, but they do most conclu- 
sively indicate that we are dealing with relations 
beyond the range of our experience ; and our at- 
tempts to represent these relations to our minds by 



NATURALNESS OF THE GOSPEL. 305 

means of ethereal media or assumed attractions re- 
semble the play of children with their dolls and toys. 

In Hke manner it is no objection to a theological 
system that it involves much that is incomprehensible 
and seemingly contradictory. The question simply 
should be, Does it give a faithful representation of 
known facts and relations? and if so, the inconsis- 
tencies indicate no more than this, that it deals 
with forms of being beyond the range of human 
experience. 

It is to me a striking evidence of the truth, as well 
as of the naturalness of the gospel narrative, that 
throughout there should be such an accommodation 
to the necessary limitations of human intelligence. 
On all occasions the truth is presented in the simplest 
material imagery, and the most tender regard is paid 
to the Marthas and Thomases of every age, to whom 
seeing could give to behef the only adequate certi- 
tude ; and when it was necessary to certify to eternal 
realities and to arouse men from their material leth- 
argy, how unaffectedly it is done with a few simple 
but grand sentences. How differently it would have 
been, how differently it has been, with every human 
teacher to whom has been opened a vision of things 
eternal. How irresistible has always been the ten- 
dency of the human mind, however enlightened, to 
dwell on all that is anomalous, incongruous, or awe- 
inspiring, in the situation described. We find this 
most markedly in the elder dispensation. We find 
it even in the vision of the Apocalypse. And is 
there not a lesson in such facts which we may well 
ponder? 



306 PARADOXES OF DOGMAS. 

In teaching physical science it would be very un- 
wise to give prominence to the difficulties of concep- 
tion on which for a special purpose we have dwelt in 
these lectures. These are real difficulties, and must 
be met by every thoughtful student sooner or later ; 
but they have no practical significance, and are 
wholly ignored in the every-day work of the labo- 
ratory. Of course no feeling is here involved, as in 
religious questions ; but with all this difference is it 
wise, in an age which is so much engrossed with ma- 
terial interests, to give prominence to similar difficul- 
ties of theological doctrine that have as little bearing 
on Christian living? Is it not better that they should 
be ignored than become hindrances to faith? and 
does not all experience teach that a faith well- 
grounded on personal experience and active benevo- 
lence will accept any doctrine once delivered to the 
saints whose holy lives it seeks to imitate? 

Our Puritan forefathers delighted in theological 
dialectics, and sought to exaggerate rather than to 
reconcile the paradoxes and contradictions of dogmas. 
They were thoughtful men of speculative dispositions, 
whom both political circumstances and sensitive con- 
sciences had debarred from the intellectual life of the 
world, and who found the chief exercise of their in- 
telligence in the discussion of theological dogmas. 
But it may be doubted whether this at times morbid 
exercise of their faculties induced any more humble 
and loving lives than those of many a devoted saint 
who never so much as heard of Foreknowledge or 
Predestination. 

In connection with the difficulties of conception 



CONTINUITY OF LIFE. 307 

which -the Christian system involves, the question of 
the Christian miracles at once suggests itself; but 
this is too large a subject to be discussed here. Two 
principles, however, which we have sought to estab- 
lish, have a bearing upon the matter. The first is 
that, with certain obvious limitations, there can be no 
prodigy in nature so wonderful that it may not be 
accepted on adequate evidence; and the second is 
that so far as our knowledge extends there is ample 
room for the appearance of new forces in the chain 
of causation. Obviously these principles, if estab- 
lished, remove in very great measure the antecedent 
presumption against miracles, and leave their authen- 
ticity to be established in every case by the evidence 
alone. In weighing evidence men will be guided by 
the self-evident truth that it is more probable that a 
witness should be deceived than that the usual order 
of nature should be altered ; and if the evidence is in 
question, the counter presumption thus created is 
overwhelming. But in the presence of well-attested 
fact all questions of probability scatter to the winds ; 
and what better attestation of an historical fact can 
you have than continuity of life? and I question if 
any one who has fully partaken of that life ever 
questioned the validity of the evidence. 

Thus the continuous Hfe of the Church from the 
beginning becomes the most convincing evidence of 
the Resurrection, that of all Christ's miracles the most 
vital to the authority and influence of His Church ; 
for " if Christ be not risen then is our preaching vain, 
and your faith is also vain." Just as the religion of 
Mahomet, as a power in history, dates from the 



308 THE RESURRECTION. 

Hegira, and, however surprising the effects ulti- 
mately produced by such gross materiahsm, presents 
a perfect continuity from the first, each step of the 
progress being natural and intelligible, — so Chris- 
tianity, as a force in society, dates from the Resur- 
rection, and shows an unbroken line of sequences 
from that event. Granted, if you demand it, that the 
Resurrection was a condescension to the conditions of 
our material existence. Explain the outward aspects 
of the event as you please. Still there remains the 
fact of history that something occurred at that time 
which produced conviction on the minds of the be- 
holders, and to which the origin of the Christian 
Church must be traced. 

The high morality of Christ's teaching cannot 
account for the founding of such a church. The 
Crucifixion destroyed all hope even in the small 
band of followers who were faithful to the last ; and 
without some remarkable attestation, Christ's teach- 
ing would have produced no more effect on the 
world than that of Socrates, or of Plato, even if the 
records had been preserved. Something must have 
occurred which changed despondency to hope, and 
which inspired the disciples with courage and enthu- 
siasm. The gospel narrative gives an explanation 
which accounts for the result. The wonderful event 
which had been predicted took place. Man could 
have no conviction except through experience, and 
the experience was furnished. 

We cannot suspect the founders of Christianity of 
deliberate falsehood, any more than we can believe 
that an event from which such great consequences 



THE RESURRECTION. 309 

immediately flowed was a myth. The witnesses must 
have believed that they saw what they described. 
Explain away the facts as you please. Regard the 
phenomena observed as purely subjective to the 
minds of those present, and the outward appearances 
as delusive, it still must be admitted that something 
occurred, either outwardly or inwardly, which pro- 
duced such a profound impression on the minds of 
the beholders as to arouse the highest enthusiasm, 
and the most unselfish devotion, the world has ever 
known ; and from which a chain of consequences has 
been forged link by link until all that is best and 
noblest of the human race has been enchained in its 
bonds of love. 

Herein lies the great wonder. The miracle was not 
wrought for us. Thank God ! we cannot investigate 
the circumstances now, or analyze all the material 
imagery that was accessory to that solemn scene. 
But of this at least we may be sure : at that time a 
new motive came into operation which changed the 
whole order of society, and to this time history points 
continuously back, as it does to Caesar crossing the 
Rubicon, or to Luther nailing his theses to the door 
of the Schlosskirche at Wittenberg. If there be such 
a thing as order in the evolution of nature this event 
was a part of that order. If there be an intelligent 
Ruler of the world this event was ordained by Him ; 
and whether He worked through methods intelligible 
to us, or by means past our finding out, and which 
with our limited knowledge and experience we call 
supernatural, the event was no less miraculous in its 
occurrence, no less wonderful in its result. 



310 THE SYMBOLISM OF CHRISTIANITY. 

Turning now to the practical working of the Chris- 
tian system, how simple are the principles of action, 
how plain the duties; and what Christian mother 
watching over her sick child, what aged saint nearing 
his rest, or what soldier of Christ in the midst of the 
conflict were ever troubled by difficulties of concep- 
tion? Our analogy here again is perfect. 

I hope further that the analogy of the symbolism 
of science may aid us to a better understanding of 
the purport of the symbolism of Christianity. We 
have endeavored to show that the symbols in 
chemistry were something more than mere conven- 
tionalism; that although absurd and grotesque if 
regarded as the exact patterns of realities, they were 
obviously the signs of an underlying truth as yet 
only dimly apprehended. How characteristic this is 
also of all the legitimate symbols of Christianity, in- 
cluding under this term much of the imagery both of 
the Old and of the New Testaments. These are pro- 
fessedly types, not likenesses of spiritual being; but 
like the symbols of science, they are aids to the im- 
agination, they give definiteness to thought, they 
give substance to things unseen. Such types, how- 
ever, must resemble in certain features their origi- 
nal, inasmuch as they form a safe basis of inference, 
and, like the symbols of science, guide the mind to 
the discovery of truth. Like the ladder seen in vis- 
ion by the patriarch at Bethel, they rest on earth, 
but they lead upwards to where the material blends 
with the spiritual in the effulgence of Divine glory. 
On the other hand, as the conventional forms of 
science often acquire an undue prominence, and be- 



GRADUAL UNFOLDING. 3II 

come invested with an imaginary concreteness in the 
thoughts of those who are constantly occupied there- 
with, so the symbolism of Christianity is also too 
frequently materialized, and the spirit that giveth 
life completely hidden by the letter that killeth. 

In all great scientific inductions which have per- 
manently raised the level of human knowledge, the 
advantage gained has never been appreciated at the 
time, and it has been the work of years to develop 
the consequences of a single lofty intellectual con- 
ception. Here again the parallelism is most striking 
with the Christian revelation. How faintly did the 
earlier disciples comprehend the work of their Mas- 
ter; and, as century after century has passed since, 
how slowly has the world come to a realization of the 
truth ; and in proportion as man has become enlight- 
ened, how steadily has the scope of the grand scheme 
widened before his enraptured vision. So also if we 
consider solely the intellectual aspects of the Chris- 
tian system, where in literature shall we find a power 
of deductive reasoning comparable with that of the 
great apostle to the Gentiles, whose boast was " Not 
as though I had already attained, either were already 
perfect, but I follow after." Pressing this analogy 
still further, we may not inaptly compare theological 
systems with the deductions of science, and like the 
last those also must abide the test of experience, and 
be judged by the united voice of that great multitude 
who have been redeemed to God " out of every 
kindred and tongue and people and nation." 

I have quite failed in one of my chief aims in these 
lectures if I have not succeeded in impressing you 



312 SENSE OF LIMITATION. 

with the strong sense which I feel of the uncertainties 
and limitations which encompass the student of na- 
ture on every side. I am well aware that such feel- 
ings as I have expressed are in part a matter of tem- 
perament, and that some men are more susceptible 
to such impressions than others. Still, your own 
knowledge of literature will sustain me in the asser- 
tion that in all that I have said I am in sympathy 
with the noblest thinkers the world has known. Un- 
numbered scholars, of whose attainments the world 
has been proud, and for whose contributions to knowl- 
edge the human race will be ever grateful, — men like 
Plato, Marcus Aurelius, Copernicus, Descartes, New- 
ton, Faraday, — have left written evidence of a more 
or less deep conviction that the intellectual life has a 
nobler destiny than the life of the body ; that there 
may be modes of existence of which ^the senses take 
no cognizance ; and that, while the things which are 
seen are temporal, the things that are unseen are 
eternal. There has always been with such minds a 
** reaching forth unto those things which are before," 
and although they may not have recognized the goal, 
a pressing "toward the mark for the prize of the 
high calling of God in Christ Jesus, . . . who 
shall change our vile body, that it may be fashioned 
like unto His glorious body, according to the work- 
ing whereby He is able to subdue all things unto 
Himself." 

How true it is now of our systems of theology as of 
our systems of science that " we know in part, and 
we prophesy in part. But when that which is per- 
fect is come, then that which is in part shall be done 



man's place in nature. 313 

away."- And how obviously the recognition of such 
limitations in our present life points beyond the veil. 
The consciousness of limitation is an evidence of 
things unseen, and thus our material hindrances 
become educators of faith. They are a law in our 
members " which is our schoolmaster to bring us 
unto Christ." 

The harmony of the Christian system with the 
methods of nature, and the force of the argument 
which rests on this analogy, nowhere appear more 
conspicuously than when studied in relation to the 
most recent of the great systems of science. Man as 
an animal is weak as compared with many of the 
higher vertebrates, and unfitted to cope with them in 
the fight for existence. Place man naked, but in the 
full command of his physical powers, in a jungle with 
tigers, or even in a forest with wildcats, and he would 
have no chance in the inevitable struggle that must 
ensue. The element of intelligence, and that alone, 
makes his superiority; and this mental endowment 
has made a comparatively weak animal the lord of 
creation. According to the new school of natural- 
ists, man's development must have begun ages back, 
when intelligence became an important factor in the 
struggle for life. Remember, however, that, as I have 
before shown, this factor may have been a preor- 
dained condition then appearing for the first time in 
the chain of causation ; and that as yet certainly we 
have no knowledge whatever which would render 
such an interference (if the preordained can be called 
an interference) either impossible or improbable; 
and further, recall the opinion then expressed that 



314 man's ancestors. 

geological evidence indicates a marked break at the 
advent of man. You may then without prejudice 
accept the necessary inference from the theory that 
man after the flesh was descended, not from any 
species now existing, but from some species far less 
fitted to cope with its surroundings than the monkey, 
the ourang, or the gorilla have become. These an- 
thropoids are not regarded as the ancestors of man ; 
but both they and man are, according to the modern 
hypothesis, descendants of a common ancestor. Man 
has remained comparatively feeble in his physical 
powers, but has gained supremacy through his in- 
telligence. The animals most like him in outward 
form and structure, not partaking of his intelligence, 
have been developed in one or another direction 
to a far higher degree; because they have had to 
wage the fight for existence with physical powers 
alone. 

In considering the influence of intelligence in the 
struggle for existence, remember that it has led men 
to combine in societies, and establish governments 
so as to protect the weak. Under such conditions, 
while man's collective power to cope with brute 
forces has been greatly increased, his individual 
power has been weakened ; and circumstances con- 
stantly remind us what a weak, miserable animal nian 
is when left to his own resources. When you con- 
sider what a delicate, helpless creature the human 
infant is, it will require no aid of poetry or art to 
show how soon the race would be extinguished if the 
human mother were left to defend her ofifspring with 
her own strength. The tales of the wilderness chiefly 



THE LEADERS OF MEN. 315 

owe their interest, as it seems to me, to the vividness 
with which they picture the features of that fierce 
and terrible warfare from which civiHzed men are so 
greatly protected through their institutions and their 
inheritances ; and they show us that even in the sav- 
age state the protection, such as it is, arising from 
association and com.bination, is equally essential to 
the continued life of the race ; thus plainly indicat- 
ing that even the feeble intelligence of the savage 
gives him an immense advantage over the brute in 
the struggle for existence. 

As intelligence has been the chief factor which has 
given the race of man its pre-eminence, so it has been 
that gift in a special degree which has given to indi- 
vidual men the power of advancing their race. The 
great men who have marked special epochs in history, 
or to whom great movements may be traced, have 
been men of great mental power in some phase or 
other, or else men endowed with unusually clear 
spiritual insight. Recall the great names of history, 
the great conquerors, the great rulers, the great law- 
givers, the great in literature, the great in art, the 
great in science, the great in philosophy, the great 
in theology, the founders of states, the founders of 
religions, the heroes, the saints, and the prophets of 
every age. Who of all these men whose names are 
household words, remembered and cherished when 
all other records of the past are forgotten, who, I say, 
has exerted the greatest influence, and produced the 
most lasting effect on the progress of mankind ? 
There can be but one answer. Theorize about the 
matter as you please, explain the influence as you 



3l6 GROWTH THE METHOD OF CREATION. 

may, by far the greatest effects ever produced in his- 
tory can be traced directly to the teaching of the one 
Man who was born of Mary in the manger at Bethle- 
hem. Frame what theories you please about His 
nature, He is, on the lowest view of His nature, the 
greatest leader of humanity. It is the reasonable 
course to accept His own theory of Himself, and to 
act upon it ; and men by acting upon it have raised 
themselves and their fellows immeasurably in the 
scale of being. 

Let us not fail to remember also in this connection 
that development, or slow growth, is plainly the 
method of creation. Nothing is more distinctly 
taught by nature than this. Every advance in knowl- 
edge only makes this truth more plain. Before Dar- 
win published his now famous work on " The Origin 
of Species," an EngHsh poet wrote : — 

" The solid earth whereon we tread 

" In tracts of fluent heat began, 

And grew to seeming random forms, 
The seeming prey to cyclic storms, 
Till at the last arose the man ; " 

and this plain teaching of geology can be supported 
by overwhelming facts from almost every department 
of knowledge. If the Bible in some passages may 
seem to imply otherwise, these passages must be in- 
terpreted by the spirit of the writing, which through- 
out enforces the reverse idea, and nowhere more 
impressively than in the teaching of Christ Himself. 
It is not, as some seem to think, a question of power 
to create, but solely a question of method. One of 



PERFECTION THROUGH SUFFERING. 317 

the most striking features in the life of Christ is His 
submission to the slow, halting, and apparently cruel 
methods of nature ; while all the time there is an evi- 
dent consciousness of power to secure the end and 
avoid the pain. When we are impatient with these 
methods, and think that they derogate from the maj- 
esty of the Almighty, let us remember that scene 
under the olives of Gethsemane, the impatience of 
the disciple, the calmness of the Master, and the 
memorable words, *' Thinkest thou that I cannot now 
pray to my Father, and He shall presently give me 
more than twelve legions of angels? " 

But although we may not without exaggeration 
push our analogy further, yet we can catch glimpses 
of a meaning still deeper than any we have as yet 
grasped; and I hope I shall be pardoned if with 
deepest reverence I allude to this obscure and terri- 
ble significance. We recognize the struggle for exist- 
ence as an agency in nature, and the naturalists 
discuss its effects as they would those of heat or 
electricity. But do they, do we, realize what is im- 
plied by these words ? They cannot ; for they would 
be staggered by the thought, and overwhelmed by 
the horror, and could not write or speak so coolly if 
they did. " For we know the whole creation groaneth 
and travaileth in pain together until now." Those 
who minister in the slums of your cities know how 
true this is ; and they will tell you that these impas- 
sioned words of St. Paul convey no adequate con- 
ception of the reality. Even fiction does not dare 
to depict faithfully the terrible death struggle, and 
art is powerless before it. If we turn pale at the 



3l8 PERFECTION THROUGH SUFFERING. 

bare recital of the horrors of the siege of Jerusalem, 
of the plague at Florence, of the hecatombs at Co- 
massie, or of the battle-fields recorded on every page 
of history, and also of the visitations of earthquake, 
shipwreck, tornado, and pestilence, which at times 
come near our own homes, and are stirred from the 
inner depths of our souls by the distant roar of the 
conflict, what must have been the ordeal through 
which our race has passed, what the sorrow and 
anguish through which every advance has been won ! 
And do we ourselves realize that our civilization, 
our education, our well-being, and all that consti- 
tutes our birthright have been purchased with so 
much blood? 

If this be true of man, the most favored of creat- 
ures, and through his intelligence the most capable 
of protecting himself, we can readily believe the 
declaration of naturalists that the destructiveness of 
the internecine warfare among the lower animals is 
wholly beyond the power of imagination to conceive. 
Swift destruction is the rule, — life, however short, the 
great exception ; and one is astonished by the enor- 
mous productiveness of nature which can people the 
earth in spite of such a drain. All naturalists are 
agreed that it is this wholesale destructiveness which 
alone gives efficacy to what is called natural selection. 
As the animal is higher in the scale of being, the 
destructiveness is less; but in the same proportion 
the suffering is greater ; and among men the capa- 
bility of suffering is almost a measure of intellectual 
and spiritual growth. As then in the struggle for 
existence perfection is reached through suffering, so 



THE MYSTERY OF PERSONALITY. 319 

in the spiritual world men rise to higher things 
through sorrow ; and though as they rise their power 
of suffering is increased, yet in the beauty of holiness 
their sorrow is at last turned into joy. " Blessed are 
they that mourn, for they shall be comforted." Thus 
the Cross becom.es the type of perfect character, as 
well as the type of deepest sorrow ; and as we pass 
beneath its shadow, nature will help to teach us the 
deep significance of those solemn words, " And if I 
be lifted up I shall draw all men unto me." 

On the quai which lines the banks of the Loire at 
Tours stands a noble statue, erected in honor of the 
greatest philosopher France has ever known; who, 
although he thought and wrought elsewhere, and died 
in a foreign land, was born in Touraine. On the 
pedestal is engraved simply 

*' RENE DESCARTES ; " 

but at the foot of the statue we read, as from the 
great man's lips, 

*' COGITO, ERGO SUM." 

Most beautifully has this famous aphorism been para- 
phrased by the great English poet whose verses I 
have several times quoted because nowhere else do 
I find so forcible an expression of the overpowering 
sense of natural phenomena which weighs on my 
own soul, but which my feeble words are powerless 
to reproduce : — 

" The baby new to earth and sky, 

What time his tender palm is pressed 



320 "COGITO, ERGO SUM." 

Against the circle of the breast, 
Has never thought that ' This is I.' 

" But as he grows he gathers much, 
And learns the use of ' I ' and ' me ' ; 
And finds ' I am not what I see, 
And other than the things I touch.' " 

The mystery of evil and the mystery of suffering 
have their counterpart in the mystery of personality. 
Science has not shed one single ray to lighten the 
darkness of either mystery. We have faith **that 
somehow good will be the final goal of ill." We 
trust that Omniscience and Free Will, Omnipotence 
and Sin, Beneficence and Suffering, will one day be 
reconciled to our intelligences ; and we look for the 
explanation to those awful necessities which an alli- 
ance of the spiritual with the material implies. Still, 
amidst all this darkness our analogy does not wholly 
fail us, and we have clear indications that the pro- 
visions of Grace are of a piece with the provisions 
of material nature. 

If there is one attribute of our being which more 
than any other marks our individual existence, it is 
the consciousness of personality ; and yet that entity 
which thinks and wills is so blended with our material 
nature that we cannot, except in thought, dissociate 
the two. The conclusion of the profoundest analysis 
which philosophy can make is still expressed in the 
three words " COGITO, ERGO SUM." Nevertheless, 
this personality is the most conspicuous fact in all 
human history, and every attempt of false science or 
of poetry to resolve or obscure it, has been wholly 



SPIRITUAL LIFE. 32 1 



vaim Personality, with its free will, is, then, an ele- 
mentary principle of nature ; and how wonderfully is 
Christianity throughout in harmony with this funda- 
mental truth. The great object of the Gospel is to 
purify and sanctify the sources from which it pro- 
ceeds, but the personal will is always left free and 
inviolate. The recorded miracles all dealt with ma- 
terial nature. Christ never constrained a human will. 
When He knew that it was to betray Him, and a 
single word would arrest the action, He allowed it 
free course ; and in the final passion — " then said 
Jesus, * Father forgive them, for they know not what 
they do.' " 

We have time for only one further thought. Man 
knows nature because he is in harmony with it ; man 
knows spiritual truth in the same way; and certitude 
in either case rests on similar evidence. Such are 
the general propositions which I have sought to 
maintain in these lectures. We have to thank the 
evolutionists for a plausible explanation of the first 
of the propositions, and they will not object if we 
apply the same principles to the second. A simple 
cell, at first only slightly sensitive to light, has devel- 
oped into that organ of wonderful adaptations, the 
eye. By the survival of the fittest, each advantage 
gained has been held and handed down; and thus 
the organ has been gradually adjusted to the environ- 
ment, and fitted to give to the mind of man truthful 
information about external objects and accurate im- 
pressions of the beauties of the outer world. So 
another cell, specially sensitive to the vibrations of 
the atmosphere, by associating with itself other sen- 



322 CONCLUSION. 



sitive cells and bequeathing every small gain by 
which the resulting structure became more respon- 
sive to the tremors of sound, has grown into that 
other organ, not less wonderful, through which the 
mind receives equally faithful impressions of har- 
mony, melody, and articulate speech. The method 
by which these results have been worked out is, 
however, a question of no importance to our argu- 
ment, so long as we all admit — as all do, evolu- 
tionists with the rest — that the capacity of these 
organs to give accurate information about the ex- 
ternal world is wholly due to their adaptation to the 
environment. 

But if man's harmony with his environment physi- 
cally is an evidence of truth, then his harmony with 
his environment spiritually must be equally so. If a 
sensitive nerve can be trusted, a sensitive conscience 
is not less trustworthy; otherwise man's mind must 
have grown into harmony with its environment in one 
relation, and not in the other. If when man longs for 
beauty and harmony the impressions which flow in 
through the eye and ear are to be trusted, then it 
must be that when in his higher moods he yearns for 
purity and righteousness and holiness, the assurances 
which come to him on his bended knees are equally 
well-founded. 

Finally, if there be any knowledge, if there be any 
truth, if there be any certainty in this mortal state 
of being, if there be any consolation in the past, any 
satisfaction in the present, any hope in the future of 
this world, it is only to be found in the spiritual life 



CONCLUSION. 323 



of man. That alone is permanent amid ceaseless 
change; that alone is satisfying amid constant sati- 
ety; that alone is comforting amid constant disap- 
pointments; that alone is sustaining amid constant 
suffering ; that alone is consoling amid constant be- 
reavement; that alone is assuring in the presence 
of death ; that alone is triumphant in the confident 
hope of immortality. And if I have been able, in 
however imperfect a way, to make more evident to 
your understanding that our power of apprehending 
spiritual things, our discernment of righteousness, 
our thirst for affection, our aspiration after purity, 
our communion with hoHness, are as truly evidences 
of external realities as any impressions of our senses ; 
and further, if it has appeared that the inductions 
based on the experiences of our spiritual life are 
just as authentic, and just as valid, as those drawn 
from material phenomena, — then I have accomplished 
the object at which alone I have aimed in these 
lectures. 

I am well aware that I have not sounded the key- 
note of theology ; but this was not my office. I was 
intrusted with the very subordinate task of sustaining 
the harmony of the refrain in which alone nature can 
join in the heavenly song; and I even fear that I 
have made my part too prominent. 

You will receive commission to preach the glad 
tidings of a risen Lord, and no more noble service 
can man render on earth. If I have in any measure 
helped to prepare your way, it is all that I could 
hope to accomplish. You are intrusted with a mes- 



524 CONCLUSION. 



sage before which all the learning of the world must 
bow. Proclaim it confidently and fearlessly, not in 
" oppositions of science falsely so-called," but in 
the name of Him who alone is " the Way, the Truth, 
and the Life." 



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